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This document discusses the Axiom of Choice (AC), a foundational principle in set theory that states that for any set of nonempty sets, there exists a function that chooses one element from each set. The document provides examples to illustrate AC with finite and infinite sets. It explains that while AC seems intuitive for finite sets, it leads to counterintuitive conclusions for infinite sets. The document also discusses the relationship between AC and Zermelo-Fraenkel set theory (ZF), noting that ZF does not prove or disprove AC, so its inclusion in ZF is a matter of mathematical preference.

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Sets PowerPoint Presentation

Sets PowerPoint Presentation

union and intersection of events.ppt

union and intersection of events.ppt

Absolute Value

Absolute Value

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Sets PowerPoint Presentation

The theory of sets was developed by German mathematician Georg Cantor in the late 19th century. Sets are collections of distinct objects, which can be used to represent mathematical concepts like numbers. There are different ways to represent sets, including listing elements within curly brackets or using set-builder notation to describe a property common to elements of the set. Basic set operations include union, intersection, and complement. Venn diagrams provide a visual representation of relationships between sets.

union and intersection of events.ppt

The document discusses probability and events, defining key terms like experiment, outcome, sample space, and event. It provides examples of simple and compound events, and explains how to calculate the probability of simple events using the formula of number of outcomes in the event over the total number of possible outcomes. Rules for probability are also outlined, such as the probability of any event being between 0 and 1 and the sum of probabilities of all outcomes equaling 1.

Absolute Value

The lesson plan summarizes teaching students how to solve linear equations and inequalities involving absolute value. It includes learning objectives, concepts, materials, strategies, and sample problems. The lesson will begin with a review of absolute value concepts and properties. Students will then work through examples of solving absolute value equations and inequalities as a class and independently. Formative assessment includes students presenting solutions on the board and a quiz to evaluate understanding. The homework assignment is to study word problems involving numbers, integers, ages, and distances.

Linear algebra-Basis & Dimension

Linear algebra
Basis & Dimension
1.Dimension of vector space
2.Dimension of subspace
3.Dimention of Quotient space

Measures of variability grouped data

Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper

Combinations

The document discusses combinations and restricted combinations. Some key points:
- Combinations refer to the number of ways of selecting items without regard to order, as opposed to permutations which consider order.
- A combination formula is given to calculate the number of combinations of n items taken r at a time.
- Examples demonstrate calculating combinations in situations like selecting committee members or players for a team when certain items must or cannot be included.
- The number of combinations when p particular items must be included is written as n-pCr-p, and when p items cannot be included is n-pCr.

Lesson Plan Sample for Grade 8

1. The lesson plan discusses relations and functions through classroom activities including a game to demonstrate examples.
2. Key concepts are defined, such as a relation being a set of ordered pairs and a function requiring each domain input to map to only one range output.
3. Examples of both relations that are functions and those that are not are analyzed, with students expected to understand the difference between one-to-one, one-to-many, and many-to-one relations.

Probability 3.4

The document discusses various counting principles including the fundamental counting principle, permutations, combinations, and probabilities. It provides examples of how to use these principles to calculate the number of possible outcomes in situations like choosing options, arranging objects in order, and selecting objects without regard to order.

Group abstract algebra

1. The document introduces groups and related concepts in mathematics.
2. It defines a group as a set with a binary operation that satisfies associativity, identity, and inverse properties. Abelian groups are groups where the binary operation is commutative.
3. Examples of groups include the complex numbers under multiplication, rational numbers under addition, and translations of the plane under composition. Subgroups are subsets of a group that are also groups under the same binary operation.

What is an axiom?

This document discusses axioms and their role in formal mathematical systems. It uses Euclid's geometry as an example, outlining his five axioms including the first axiom that there is exactly one straight line between any two points. Definitions are distinguished from axioms. Contradictions to axioms may indicate either a logical error or that a different mathematical system is being described. The document concludes by promising to discuss Euclid's fifth postulate in more depth.

Sets and venn diagrams

This document discusses sets and Venn diagrams. It defines what a set is and provides examples of sets. It describes subsets and operations that can be performed on sets such as intersection, union, complement, and difference. It explains Venn diagrams and how they are used to represent relationships between sets such as disjoint, overlapping, union, and intersection. Examples are provided to demonstrate operations on sets and drawing Venn diagrams.

5.4 mathematical induction

The document discusses the method of mathematical induction. It is used to verify infinitely many related statements without checking each one individually. As an example, it examines the statement that the sum of the first n odd numbers equals n^2 for all natural numbers n. It shows the base case of this statement is true, and if the statement is true for an arbitrary n, it must also be true for n+1. Therefore, by the principle of mathematical induction, the statement is true for all natural numbers n.

Lesson Plan on Basic concept of probability

This document provides a lesson plan for teaching basic concepts of probability to 8th grade math students. The lesson plan outlines the intended learning outcomes, learning content from reference materials, learning experiences including examples and practice problems, and an evaluation and assignment. Students will learn to define key probability terms like experiment, outcome, sample space and event. They will practice identifying sample spaces for scenarios like rolling dice, coin tosses, and family compositions. The lesson aims to help students interpret probabilities and count outcomes through diagrams and systematic listing.

Chapter 1, Sets

Set theory is a branch of mathematics that studies sets and their properties. A set is a collection of distinct objects, which can include numbers, points, or other sets. Some key concepts in set theory include:
- Membership and subsets, where an object is a member of a set and a set is a subset of another if all its members are also in the other set.
- Binary operations on sets like union, intersection, and complement/difference.
- The power set, which contains all possible subsets of a given set.
- Finite and infinite sets, with finite sets having a definite number of members and infinite sets not having an end. The empty set contains no members.

Set Operations

The document discusses set operations including union, intersection, difference, complement, and disjoint sets. It provides formal definitions and examples for each operation. Properties of the various operations are listed, such as the commutative, associative, identity, and domination laws. Methods for proving set identities are also described.

Sets

A Brief introduction to set and sets types. in very simple method that can every one enjoy during study.
#inshallah.

SET THEORY

This document provides an overview of basic set theory concepts including defining and representing sets, the number of elements in a set, comparing sets, subsets, and operations on sets including union and intersection. Key points covered are defining a set as a collection of well-defined objects, representing sets using listing, defining properties, or Venn diagrams, defining the cardinal number of a set as the number of elements it contains, comparing sets as equal or equivalent based on elements, defining subsets as sets contained within other sets, and defining union as the set of elements in either set and intersection as the set of elements common to both sets.

Abstract algebra i

The document appears to be lecture notes on abstract algebra that cover topics including groups, rings, fields, and Galois theory. It begins with an introduction discussing the author's early interest in solving polynomial equations and motivation for studying abstract algebra. It then provides a brief review of properties of integers, including the division algorithm, greatest common divisors, least common multiples, and Euclid's algorithm. The notes state that these integer properties will be useful since group theory makes use of them. It introduces the topic of groups by defining binary operations and stating that certain choices will make a set into a group while others will not.

A detailed lesson plan in permutation

The document is a detailed lesson plan for a mathematics class on permutation. It outlines the objectives, content, materials, and procedures for the lesson. The lesson will teach students about permutation rules including n!, nPr, and arrangements of distinct objects. Example problems are provided to demonstrate each rule, and students will complete activities in groups to practice the rules and verify their understanding.

Lesson plan in mathematics 9 (illustrations of quadratic equations)

The lesson plan outlines a lesson on quadratic equations. It introduces quadratic equations and their standard form of ax2 + bx + c = 0. Examples are provided to illustrate how to write quadratic equations in standard form given values of a, b, and c or when expanding multiplied linear expressions. Students complete an activity identifying linear and quadratic equations. They are then assessed by writing equations in standard form and identifying the values of a, b, and c.

Sets PowerPoint Presentation

Sets PowerPoint Presentation

union and intersection of events.ppt

union and intersection of events.ppt

Absolute Value

Absolute Value

Linear algebra-Basis & Dimension

Linear algebra-Basis & Dimension

Measures of variability grouped data

Measures of variability grouped data

Combinations

Combinations

Lesson Plan Sample for Grade 8

Lesson Plan Sample for Grade 8

Probability 3.4

Probability 3.4

Group abstract algebra

Group abstract algebra

What is an axiom?

What is an axiom?

Sets and venn diagrams

Sets and venn diagrams

5.4 mathematical induction

5.4 mathematical induction

Lesson Plan on Basic concept of probability

Lesson Plan on Basic concept of probability

Chapter 1, Sets

Chapter 1, Sets

Set Operations

Set Operations

Sets

Sets

SET THEORY

SET THEORY

Abstract algebra i

Abstract algebra i

A detailed lesson plan in permutation

A detailed lesson plan in permutation

Lesson plan in mathematics 9 (illustrations of quadratic equations)

Lesson plan in mathematics 9 (illustrations of quadratic equations)

The Mathematical Universe in a Nutshell

It gives me great comfort to visualize this universe as the surface of an ever expanding four-dimensional sphere originating from a distant, but finite, past and growing indefinitely for ever. In this idealized model it easy to calculate the age of the universe by observing the velocity of the receding stars and also to make several other interesting conclusions. For more details, continue reading the presentation.

mechanizing reasoning

Humans have been attempting to mechanize reasoning for thousands of years through formal axiomatic systems like those developed by Aristotle and Euclid. Euclid's system of geometry based on five axioms and five inference rules was able to prove hundreds of propositions, but was incomplete as it could not derive all true statements. Later systems by Frege, Russell, and Whitehead attempted to develop complete and consistent axiomatic systems but were hindered by paradoxes like Russell's paradox, which showed that certain self-referential statements could not be consistently defined.

Presentation X-SHS - 27 oct 2015 - Topologie et perception

This document discusses the relationship between mathematics, perception, and cognition from multiple perspectives. It covers topics like:
- Pythagoras' and Fourier's views that mathematics compensates for the imperfection of the senses.
- Aristotle, Poincare, and others' ideas that experience and perception have a mathematical basis in principles like non-contradiction.
- Models of associative memory and complex energy landscapes from fields like neural networks and statistical mechanics.
- Geometry, from Euclid to Einstein's general relativity, and its relationship to perception through ideas like projective geometry and invariance under transformation groups.
- Information theory and its connections to measure theory and set theory through concepts like

Zeno paradoxes

Zeno of Elea developed several paradoxes to argue against the concept of motion and plurality. The paradoxes include:
1) Achilles and the tortoise paradox which argues that Achilles can never overtake the tortoise due to the infinite divisibility of space and time.
2) The dichotomy paradox which argues that before reaching any distance, one must first reach the halfway point, and before that the quarter way point, and so on ad infinitum.
3) The arrow paradox which argues that at an instant of time, an arrow must be either moving or at rest, but cannot be both, so motion is impossible.
The plurality paradoxes argue that a group of objects cannot

paper publication

https://utilitasmathematica.com/index.php/Index
Our Journal has steadfast in its commitment to promoting justice, equity, diversity, and inclusion within the realm of statistics. Through collaborative efforts and a collective dedication to these principles, we believe in building a statistical community that not only advances the profession. Paper publication

Matricų kombinatorikos taikymas automatų rūšiavimui ir NP ir P automatų klasi...

Matricų kombinatorikos taikymas automatų rūšiavimui ir NP ir P automatų klasi...Lietuvos kompiuterininkų sąjunga

Dr. Andrius Kulikauskas proposes applying matrix combinatorics to classify and study automata based on their computational capabilities. He suggests a universal framework using matrix operations that can generate all types of automata, from finite state automata to Turing machines. This framework uses operations like matrix multiplication and cycle removal to model the different automata in a way that only increases complexity. Studying this may help determine if certain computationally difficult problems can be solved efficiently by nondeterministic machines through guessing, or if they require exponential resources deterministically.Category Theory made easy with (ugly) pictures

Introduction to very basic Category Theory blending rigorous definitions with pictorial intuition and Haskell code

Euclids postulates

Euclid was a Greek mathematician from Alexandria known as the "Father of Geometry". In his influential work Elements, he deduced the principles of Euclidean geometry from 5 postulates (axioms) for plane geometry related to drawing lines and circles. The postulates state that a line can be drawn between any two points, a line can be extended indefinitely, a circle can be drawn with any center and radius, all right angles are equal, and if two lines intersect another such that the interior angles on the same side sum to less than two right angles, the two lines will intersect on that side. Euclid's work was foundational and served as the main geometry textbook for over 2000 years.

Standrewstalk

This document discusses different views on doing mathematics, including studying things at a maximal level of generality (Grothendieck view) or focusing on examples (Thurston view). It then proposes combining these views by studying collections of events and phenomena (Pascal's view). The rest of the document explores this idea of studying "generic" or typical properties that emerge when considering random or generic examples of mathematical objects like matrices, groups, graphs, and manifolds. Several specific results are mentioned, but many open questions remain about computing properties of random higher-dimensional or more complex objects.

Basics of set theory

This document provides an introduction to set theory. It discusses that sets provide a useful vocabulary in mathematics and were originally studied by Georg Cantor in the late 19th century. Most mathematicians accept set theory as a foundation for mathematics, where all mathematical objects can be defined as sets. The document then discusses different ways to define sets, including listing elements, using properties to describe elements, and examples of common sets like real numbers and integers. It notes some key concepts like subsets, empty sets, and power sets. Finally, it discusses paradoxes that arise from naive set theory, such as Russell's paradox.

Fractals, Geometry of Nature and Logistic Model

Fractals are geometric shapes that exhibit self-similarity and complex patterns at every scale. Koch's snowflake is a famous fractal where the perimeter tends towards infinity as more iterations are done, even as the area approaches a limit. The Mandelbrot set is another well-known fractal that maps the behavior of values of c under a complex iterative function, resulting in diverse patterns when zooming in. Fractals are found throughout nature in shapes like clouds, coastlines, and Romanesco broccoli. They can also be generated through computer programs and used in applications like diagnosing skin cancer.

lect14-semantics.ppt

This document discusses logical representations of natural language. It introduces lambda calculus as a way to represent functions without names. Common logical connectives like AND, OR, and quantifiers like FOR ALL and THERE EXISTS are explained. The document also discusses using constants to represent objects and predicates in a logical language. Finally, it provides an example of how to logically represent the sentence "Gilly swallowed a goldfish" using a quantifier since "goldfish" refers to an unspecified entity.

True but Unprovable

Logicians sometimes talk about sentences being “true but unprovable." What does this mean? This presentation includes a fairly thorough introduction to mathematical logic.

Prolog 01

This document provides an introduction to Prolog programming through examples of syllogisms and modeling logic problems. It discusses SWI-Prolog, facts and rules, queries, variables, structures, predicates, programs, and modeling change. Key concepts are summarized such as backward chaining, cuts, dynamic facts, and modeling "real life" problems through games and adventure programs. The document uses a dragon adventure game to demonstrate Prolog programming concepts in action.

Fractals

Fractals are irregular patterns that are self-similar across different scales. They are a branch of mathematics concerned with shapes found in nature that have non-integer dimensions. Some early contributors to fractal concepts included Leibiz, Cantor, and Hausdorff, but it was Mandelbrot who coined the term "fractal" and brought greater attention to the field. One of the most basic and important fractals is the Mandelbrot set, which is a set of complex numbers that fulfill certain recursive conditions. Fractals can also be classified based on their level of self-similarity, from exact to statistical self-similarity. Fractals are found throughout nature and have applications in fields like astrophysics

Albert Einstein (2) Relativity Special And General Theory

This document provides instructions for classifying ebooks based on their file format and subject matter. It specifies that:
1) Ebooks should be in Adobe PDF or Tomeraider format, with txt files not considered ebooks.
2) The file name should include the classification in parenthesis - (ebook - File Format - Subject Matter).
3) The subject matter classification should be one of: Biography, Children, Fiction, Food, Games, Government, Health, Internet, Martial-Arts, Mathematics, Other, Programming, Reference, Religious, Science, Sci-Fi, Sex, or Software.
This standardization of ebook file names helps groups like Fink Crew

The quantum strategy of completeness

The Gödel incompleteness can be modeled on the alleged incompleteness of quantum mechanics
Then the proved and even experimentally confirmed completeness of quantum mechanics can be reversely interpreted as a strategy of completeness as to the foundation of mathematics
Infinity is equivalent to a second and independent finiteness
Two independent Peano arithmetics as well as one single Hilbert space as an unification of geometry and arithmetic are sufficient to the self-foundation of mathematics
Quantum mechanics is inseparable from the foundation of mathematics and thus from set theory particularly

Second_Update_to my 2013 Paper

This document discusses exploring different mathematical structures as potential candidates for the geometry of the physical universe. It begins by summarizing a previous paper exploring finite geometry approaches. The document then outlines a proposed method for attempting to locate the simplest mathematical structure that could describe the universe, and iteratively making small modifications to better match observations. As a starting point, it examines some "seven day creation stories", each beginning with a simple structure like sets and applying operations each day to generate more complex structures, with the goal of reaching a structure complex enough to shed light on theories like finite M-theory. It aims to provide visual feedback on candidate geometries using computer graphics to help guide the search.

Dialectica and Kolmogorov Problems

The document discusses finding the right abstractions for reasoning problems. It describes Andreas Blass' insight about a category called PV that models problems and reductions between them. PV objects are binary relations representing problems, with morphisms describing reductions. The talk discusses using this framework and Dialectica categories to model Kolmogorov's theory of problems from 1932 and Veloso's theory. It provides examples of modeling geometry and tangent plane problems as Kolmogorov problems and reductions between them.

The Many Worlds of Quantum Mechanics

The document provides an overview of quantum mechanics, beginning with classical mechanics and the idea of a deterministic "clockwork universe." It then discusses early hints of quantum theory and how the field developed in the 1920s. Key aspects of quantum mechanics are introduced, such as the wave function, superposition, interference, entanglement, and decoherence. Measurement in quantum mechanics is discussed, as are different interpretations like Copenhagen and Many Worlds. The document uses examples like the behavior of a cat to help illustrate various quantum concepts.

The Mathematical Universe in a Nutshell

The Mathematical Universe in a Nutshell

mechanizing reasoning

mechanizing reasoning

Presentation X-SHS - 27 oct 2015 - Topologie et perception

Presentation X-SHS - 27 oct 2015 - Topologie et perception

Zeno paradoxes

Zeno paradoxes

paper publication

paper publication

Matricų kombinatorikos taikymas automatų rūšiavimui ir NP ir P automatų klasi...

Matricų kombinatorikos taikymas automatų rūšiavimui ir NP ir P automatų klasi...

Category Theory made easy with (ugly) pictures

Category Theory made easy with (ugly) pictures

Euclids postulates

Euclids postulates

Standrewstalk

Standrewstalk

Basics of set theory

Basics of set theory

Fractals, Geometry of Nature and Logistic Model

Fractals, Geometry of Nature and Logistic Model

lect14-semantics.ppt

lect14-semantics.ppt

True but Unprovable

True but Unprovable

Prolog 01

Prolog 01

Fractals

Fractals

Albert Einstein (2) Relativity Special And General Theory

Albert Einstein (2) Relativity Special And General Theory

The quantum strategy of completeness

The quantum strategy of completeness

Second_Update_to my 2013 Paper

Second_Update_to my 2013 Paper

Dialectica and Kolmogorov Problems

Dialectica and Kolmogorov Problems

The Many Worlds of Quantum Mechanics

The Many Worlds of Quantum Mechanics

The importance of being human 3

What makes us humans different from animals? Culture? The ability to make tools? The language? Morality? Art? This presentation will show us that these criteria alone are not enough to explain what makes us different from animals.

Can christian schools continue to teach only about traditional marriage

An approach to the big general issue whether faith schools should be allowed to teach based on their fundamental beliefs and discriminate amongst teachers and students because of their faith.

The unlimited desire IIS2019

1. The document discusses three potential traits that define humanity: understanding and language, freedom and self-responsibility, and unlimited desire.
2. It argues that unlimited desire, which drives humans to constantly search for meaning, happiness, and fulfillment through questions, choices, love and communion, may be the most fundamental human trait.
3. This trait of unlimited desire can justify fundamental personal rights like the right to life, freedom, and due process, which in turn other rights are derived from, in order to ensure humans can fulfill their desires. However, recognizing another's humanity ultimately requires choice and acknowledgement of their desires too.

Causality from outside Time

Causality from outside Time
Alfred Driessen
Talk presented at the 21th International Interdisciplinary Seminar, Science and Society: Defining what is human
Netherhall House, London, 5-1-2019
Content
Introduction
Time in Relativity
Time in Quantum Mechanics
Conclusions
Conclusions from this study:
There are causes beyond the realm of science,
- they are not observable by physical or scientific means
- the effects of these causes, however, are observable by physical and scientific means.
Physics is not complete.

Can computers replace teachers?

The presentation has two parts. In the first one, we review a series of studies that compare the efficacy of learning with "digital teachers" as opposed to learning with normal teachers. In the second part, we make several considerations from different points of view that may be helpful to answer the question.

Future contingents and the Multiverse

1) The document discusses future contingencies and the multiverse perspective from Antoine Suarez combining two philosophical views.
2) It describes Ernst Specker's work on quantum contextuality and includes photos of Specker with his son and colleague Simon Kochen.
3) Suarez identifies Hugh Everett's many worlds theory with thoughts in the "mind of God", finding a way to incorporate a deity into the picture according to a quote in Nature.

The CRISPR/CAS9 genome editing system and humans

This is a brief introduction to the CRISPR/Cas9 genome editing technique and a quick review of two articles that have to do with potential applications in humans. There is a draft for an ethical reflexion.

Achilles, the Tortoise and Quantum Mechanics

Achilles, the Tortoise and Quantum Mechanics
Alfred Driessen
prof. emer. University of Twente
In several places of his Physica Aristotle analyzes the famous antimony of Zeno about the competition between Achilles and the Tortoise. He emphasizes that any movement, or more general any change, is actually a continuum, i.e. an unity. It depends on the specific movement or change whether this continuum is potentially divisible in parts. In fact, there could be certain minima of the division. In line with this approach, Quantum Mechanics states that there are minima or quanta of movement (or change), with other words, there are no gradual changes in the world of micro- and nano-structures. This behavior is completely unexpected when starting with the mechanistic approach of classical physics.
Taking another finding of Aristotle, the four aspects of causality including final cause, one gets another ingredient of Quantum Mechanics. Movements and changes are not only influenced by the initial state -describing the present situation- but also by the final state which takes account of the future situation. As an example one may mention Fermi’s golden rule, where the initial and final state symmetrically determine the transition probability.
Bringing these two philosophical concepts of Aristotle together namely quanta of movement and final cause, a new light is shed on fundamental issues in Quantum Mechanics. One may mention the experimental evidence for contextuality, which is considered one of the weird phenomena in Quantum Mechanics. As illustration, some of the examples of experiments with optical microresonators are given.
This talk has been presented at the 20th International Interdisciplinary Seminar "Can Science and Technology Shape a New Humanity", Netherhall House, London, 5-1-2018

Transpostgenderism 5 jean_davidponci

This document discusses transhumanism and postgenderism. It summarizes views from gender studies that gender is more a social construct than biological essentialism. It explores how technologies may enable a postgender society without the gender binary, including artificial wombs, drugs controlling sexual behaviors and bonding, genetic engineering to change sex, and robots for sexual needs. However, the document concludes that pursuing postgenderism through technologies may dehumanize humanity and lose the richness of gender complementarity.

Transhumanism and brain

This presentation lists some brain-computer interface technologies that exist today and that could be attainable in future. At the end, philosophical comments about this kind of technology and transhumanism are purposed, in order to reveal the key difference between a humain brain and artificial intelligence.

Transhumanism and brain

The document discusses transhumanism and compares human and artificial intelligence. It covers current technologies like mini antennas and potential future technologies like telepathy and neuroreality. It then compares how humans and artificial systems learn, with humans able to reach an understanding of essence while artificial intelligence relies on computational power. The document concludes that hard transhumanism, with robots becoming the dominant lifeform, clashes with philosophical views, while soft transhumanism involves more integration between humans and robots but maintains humans as the primary agents.

Netherhall 2018 m fox

The document discusses experimental attempts to realize quantum computers. It begins with an introduction to quantum technologies and quantum bits or qubits. It then describes the current state of the art in quantum computing technologies, including ion traps, superconducting circuits, and linear optic quantum computing. The document provides examples of single qubit gates and two-qubit gates needed to build a universal quantum computer. It also summarizes different physical systems used to implement qubits and discusses challenges in scaling up quantum computers.

Sequential processing in nature

1. The document discusses the differences between sequential processing in nature compared to scientific computation. Protein folding occurs sequentially and efficiently in nature, while computation relies on approximation and linearization.
2. Artificial neural networks provide some similarities to natural processes by using weighted connections between nodes, but training requires vast resources compared to natural systems.
3. Quantum computing may provide solutions in a way analogous to how nature appears to "know" the right protein folding solution, but this ability is not well understood.

Infinite Chess: winning and draw

A presentation about Infinite Chess and the difference between man and machines. From works by C.D.A. Evans and J.D. Hamkins. Presented during the International Interdisciplinary Seminar of London, January 2018.

The importance of being human 3

The importance of being human 3

Can christian schools continue to teach only about traditional marriage

Can christian schools continue to teach only about traditional marriage

The unlimited desire IIS2019

The unlimited desire IIS2019

Causality from outside Time

Causality from outside Time

Can computers replace teachers?

Can computers replace teachers?

Future contingents and the Multiverse

Future contingents and the Multiverse

The CRISPR/CAS9 genome editing system and humans

The CRISPR/CAS9 genome editing system and humans

Achilles, the Tortoise and Quantum Mechanics

Achilles, the Tortoise and Quantum Mechanics

Transpostgenderism 5 jean_davidponci

Transpostgenderism 5 jean_davidponci

Transhumanism and brain

Transhumanism and brain

Transhumanism and brain

Transhumanism and brain

Netherhall 2018 m fox

Netherhall 2018 m fox

Sequential processing in nature

Sequential processing in nature

Infinite Chess: winning and draw

Infinite Chess: winning and draw

Gasification and Pyrolyssis of plastic Waste under a Circular Economy perpective

Review on Gasification LCA. Presentation given by Cecilia Hofmann at Advanced Recycling Conference in Cologne, 2023.

Bragg Brentano Alignment for D4 with LynxEye Rev3.pptx

Bragg Brentano Alignment for D4 with LynxEye

Introduction to Space (Our Solar System)

Space is tremendous, apparently endless span that exists past earth and its environment. It is a locale up with endless heavenly bodies,
including stars, planets, moons, space rocks, and comets, all represented by the gravity. Space investigation has extended how we might interpret the universe, uncovering the excellence and intricacy of far off cosmic system, the secret of dark openings, and the potential for life past our planet. An outskirts keeps of motivating interest, logical request, and a feeling of marvel about our spot in the universe. Space is immense, largely unexplored expanse beyond Earth's atmosphere, home to countless celestial bodies likes stars, planets, and asteroids. Human exploration began with the launch of Sputnik in 1957 followed by significant achievements such as the Moon landing in 1969.

How Does TaskTrain Integrate Workflow and Project Management Efficiently.pdf

In today's dynamic business environment, managing project management workflows
efficiently is crucial for maintaining operational excellence and achieving strategic goals.
Workflow project management is two interconnected aspects of running a successful
business, and the right software solution can make all the difference. TaskTrain is a standout
tool that integrates workflow and project management seamlessly, offering a comprehensive
solution that enhances productivity, collaboration, and efficiency. In this blog, we’ll explore
how TaskTrain excels in integrating these critical functions, ensuring that your projects run
smoothly and your workflows are optimized.

Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY

A REVIEW ON RADIOISOTOPES IN CANCER THERAPY

Transmission Spectroscopy of the Habitable Zone Exoplanet LHS 1140 b with JWS...

LHS 1140 b is the second-closest temperate transiting planet to the Earth with an equilibrium temperature low enough to support surface liquid water. At 1.730±0.025 R⊕, LHS 1140 b falls within
the radius valley separating H2-rich mini-Neptunes from rocky super-Earths. Recent mass and radius
revisions indicate a bulk density significantly lower than expected for an Earth-like rocky interior,
suggesting that LHS 1140 b could either be a mini-Neptune with a small envelope of hydrogen (∼0.1%
by mass) or a water world (9–19% water by mass). Atmospheric characterization through transmission
spectroscopy can readily discern between these two scenarios. Here, we present two JWST/NIRISS
transit observations of LHS 1140 b, one of which captures a serendipitous transit of LHS 1140 c. The
combined transmission spectrum of LHS 1140 b shows a telltale spectral signature of unocculted faculae (5.8 σ), covering ∼20% of the visible stellar surface. Besides faculae, our spectral retrieval analysis
reveals tentative evidence of residual spectral features, best-fit by Rayleigh scattering from an N2-
dominated atmosphere (2.3 σ), irrespective of the consideration of atmospheric hazes. We also show
through Global Climate Models (GCM) that H2-rich atmospheres of various compositions (100×, 300×,
1000×solar metallicity) are ruled out to >10 σ. The GCM calculations predict that water clouds form
below the transit photosphere, limiting their impact on transmission data. Our observations suggest
that LHS 1140 b is either airless or, more likely, surrounded by an atmosphere with a high mean molecular weight. Our tentative evidence of an N2-rich atmosphere provides strong motivation for future
transmission spectroscopy observations of LHS 1140 b.

Travis Hills of Minnesota Sets a New Standard in Carbon Credits With Livestoc...

Travis Hills of Minnesota is revolutionizing the carbon credit industry with a unique approach that underscores both transparency and value. Unlike conventional carbon credits, Travis ensures that each credit generated by Livestock Water & Energy is meticulously verified and validated. Each credit is assigned a distinct serial number, enhancing its authenticity and marketability. This unique feature provides traceability and accountability, instilling confidence among buyers and investors. Moreover, the rigorous verification process ensures that the credits meet stringent international standards, making them highly sought after in global carbon markets.

ANTIGENS_.pptx ( Ranjitha SL) PRESENTATION SLIDE

Antigen, properties, types, epitope and paratopes, hapten, factor Influenceing antigens, tests , importance

The Dynamical Origins of the Dark Comets and a Proposed Evolutionary Track

So-called ‘dark comets’ are small, morphologically inactive near-Earth objects
(NEOs) that exhibit nongravitational accelerations inconsistent with radiative
effects. These objects exhibit short rotational periods (minutes to hours), where
measured. We find that the strengths required to prevent catastrophic disintegration are consistent with those measured in cometary nuclei and expected in
rubble pile objects. We hypothesize that these dark comets are the end result
of a rotational fragmentation cascade, which is consistent with their measured
physical properties. We calculate the predicted size-frequency distribution for
objects evolving under this model. Using dynamical simulations, we further
demonstrate that the majority of these bodies originated from the 𝜈6
resonance,
implying the existence of volatiles in the current inner main belt. Moreover, one of
the dark comets, (523599) 2003 RM, likely originated from the outer main belt,
although a JFC origin is also plausible. These results provide strong evidence
that volatiles from a reservoir in the inner main belt are present in the near-Earth
environment.

LOB LOD LOQ for method validation in laboratory

limits of detection, quantification and blank

Possible Anthropogenic Contributions to the LAMP-observed Surficial Icy Regol...

This work assesses the potential of midsized and large human landing systems to deliver water from their exhaust
plumes to cold traps within lunar polar craters. It has been estimated that a total of between 2 and 60 T of surficial
water was sensed by the Lunar Reconnaissance Orbiter Lyman Alpha Mapping Project on the floors of the larger
permanently shadowed south polar craters. This intrinsic surficial water sensed in the far-ultraviolet is thought to be
in the form of a 0.3%–2% icy regolith in the top few hundred nanometers of the surface. We find that the six past
Apollo Lunar Module midlatitude landings could contribute no more than 0.36 T of water mass to this existing,
intrinsic surficial water in permanently shadowed regions (PSRs). However, we find that the Starship landing
plume has the potential, in some cases, to deliver over 10 T of water to the PSRs, which is a substantial fraction
(possibly >20%) of the existing intrinsic surficial water mass. This anthropogenic contribution could possibly
overlay and mix with the naturally occurring icy regolith at the uppermost surface. A possible consequence is that
the origin of the intrinsic surficial icy regolith, which is still undetermined, could be lost as it mixes with the
extrinsic anthropogenic contribution. We suggest that existing and future orbital and landed assets be used to
examine the effect of polar landers on the cold traps within PSRs

smallintestinedisorders-causessymptoms-240626042532-363e8392.pptx

Small intestine, peristaltic movements

El Nuevo Cohete Ariane de la Agencia Espacial Europea-6_Media-Kit_english.pdf

Europe must have autonomous access to space to realise its ambitions on the world stage and
promote knowledge and prosperity.
Space is a natural extension of our home planet and forms an integral part of the infrastructure
that is vital to daily life on Earth. Europe must assert its rightful place in space to ensure its
citizens thrive.
As the world’s second-largest economy, Europe must ensure it has secure and autonomous access to
space, so it does not depend on the capabilities and priorities of other nations.
Europe’s longstanding expertise in launching spacecraft and satellites has been a driving force behind
its 60 years of successful space cooperation.
In a world where everyday life – from connectivity to navigation, climate and weather – relies on
space, the ability to launch independently is more important than ever before. With the launch of
Ariane 6, Europe is not just sending a rocket into the sky, we are asserting our place among the
world’s spacefaring nations.
ESA’s Ariane 6 rocket succeeds Ariane 5, the most dependable and competitive launcher for decades.
The first Ariane rocket was launched in 1979 from Europe’s Spaceport in French Guiana and Ariane 6 will continue the adventure.
Putting Europe at the forefront of space transportation for nearly 45 years, Ariane is a triumph of engineering and the prize of great European industrial and political
cooperation. Ariane 1 gave way to more powerful versions 2, 3 and 4. Ariane 5 served as one of the world’s premier heavy-lift rockets, putting single or multiple
payloads into orbit – the cargo and instruments being launched – and sent a series of iconic scientific missions to deep space.
The decision to start developing Ariane 6 was taken in 2014 to respond to the continued need to have independent access to space, while offering efficient
commercial launch services in a fast-changing market.
ESA, with its Member States and industrial partners led by ArianeGroup, is developing new technologies for new markets with Ariane 6. The versatility of Ariane 6
adds a whole new dimension to its very successful predecessors

Collaborative Team Recommendation for Skilled Users: Objectives, Techniques, ...

Collaborative team recommendation involves selecting users with certain skills to form a team who will, more likely than not, accomplish a complex task successfully. To automate the traditionally tedious and error-prone manual process of team formation, researchers from several scientific spheres have proposed methods to tackle the problem. In this tutorial, while providing a taxonomy of team recommendation works based on their algorithmic approaches to model skilled users in collaborative teams, we perform a comprehensive and hands-on study of the graph-based approaches that comprise the mainstream in this field, then cover the neural team recommenders as the cutting-edge class of approaches. Further, we provide unifying definitions, formulations, and evaluation schema. Last, we introduce details of training strategies, benchmarking datasets, and open-source tools, along with directions for future works.

MCQ in Electrostatics. for class XII pptx

Physics Multiple choice questions and answers with explanation. (Class XII Physics TN State board)

Testing the Son of God Hypothesis (Jesus Christ)

Instead of answering the God hypothesis, we investigate the Son of God hypothesis. We developed our own methodology to deal with existential statements instead of universal statements unlike science. We discuss the existence of the supernaturals and found that there are strong evidence for it. Given that supernatural exists, we report on miracles investigated in the past related to the Son of God. A Bayesian methodology is used to calculate the combined degree of belief of the Son of God Hypothesis. We also report the testing of occurrences of words/numbers in the Bible to suggest the likelihood of some special numbers occurring, supporting the Son of God Hypothesis. We also have a table showing the past occurrences of miracles in hundred year periods for about 1000 years. Miracles that we have looked at include Shroud of Turin, Eucharistic Miracles, Marian Apparitions, Incorruptible Corpses, etc.

Modelling, Simulation, and Computer-aided Design in Computational, Evolutiona...

Modelling, Simulation, and Computer-aided Design in Computational, Evolutiona...University of Maribor

Slides from:
Aleš Zamuda:
Modelling, Simulation, and Computer-aided Design in Computational, Evolutionary, Supercomputing, and Intelligent Systems.
Central European Exchange Program for University Studies (CEEPUS). TU Graz, Austria
OeAD Austria, CEEPUS network ``Modelling, Simulation and Computer-aided Design in Engineering and Management''A slightly oblate dark matter halo revealed by a retrograde precessing Galact...

The shape of the dark matter (DM) halo is key to understanding the
hierarchical formation of the Galaxy. Despite extensive eforts in recent
decades, however, its shape remains a matter of debate, with suggestions
ranging from strongly oblate to prolate. Here, we present a new constraint
on its present shape by directly measuring the evolution of the Galactic
disk warp with time, as traced by accurate distance estimates and precise
age determinations for about 2,600 classical Cepheids. We show that the
Galactic warp is mildly precessing in a retrograde direction at a rate of
ω = −2.1 ± 0.5 (statistical) ± 0.6 (systematic) km s−1 kpc−1 for the outer disk
over the Galactocentric radius [7.5, 25] kpc, decreasing with radius. This
constrains the shape of the DM halo to be slightly oblate with a fattening
(minor axis to major axis ratio) in the range 0.84 ≤ qΦ ≤ 0.96. Given the
young nature of the disk warp traced by Cepheids (less than 200 Myr), our
approach directly measures the shape of the present-day DM halo. This
measurement, combined with other measurements from older tracers,
could provide vital constraints on the evolution of the DM halo and the
assembly history of the Galaxy.

Gasification and Pyrolyssis of plastic Waste under a Circular Economy perpective

Gasification and Pyrolyssis of plastic Waste under a Circular Economy perpective

Bragg Brentano Alignment for D4 with LynxEye Rev3.pptx

Bragg Brentano Alignment for D4 with LynxEye Rev3.pptx

Introduction to Space (Our Solar System)

Introduction to Space (Our Solar System)

How Does TaskTrain Integrate Workflow and Project Management Efficiently.pdf

How Does TaskTrain Integrate Workflow and Project Management Efficiently.pdf

Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY

Review Article:- A REVIEW ON RADIOISOTOPES IN CANCER THERAPY

SCIENCEgfvhvhvkjkbbjjbbjvhvhvhvjkvjvjvjj.pptx

SCIENCEgfvhvhvkjkbbjjbbjvhvhvhvjkvjvjvjj.pptx

Transmission Spectroscopy of the Habitable Zone Exoplanet LHS 1140 b with JWS...

Transmission Spectroscopy of the Habitable Zone Exoplanet LHS 1140 b with JWS...

Travis Hills of Minnesota Sets a New Standard in Carbon Credits With Livestoc...

Travis Hills of Minnesota Sets a New Standard in Carbon Credits With Livestoc...

ANTIGENS_.pptx ( Ranjitha SL) PRESENTATION SLIDE

ANTIGENS_.pptx ( Ranjitha SL) PRESENTATION SLIDE

[1] Data Mining - Concepts and Techniques (3rd Ed).pdf

[1] Data Mining - Concepts and Techniques (3rd Ed).pdf

The Dynamical Origins of the Dark Comets and a Proposed Evolutionary Track

The Dynamical Origins of the Dark Comets and a Proposed Evolutionary Track

LOB LOD LOQ for method validation in laboratory

LOB LOD LOQ for method validation in laboratory

Possible Anthropogenic Contributions to the LAMP-observed Surficial Icy Regol...

Possible Anthropogenic Contributions to the LAMP-observed Surficial Icy Regol...

smallintestinedisorders-causessymptoms-240626042532-363e8392.pptx

smallintestinedisorders-causessymptoms-240626042532-363e8392.pptx

El Nuevo Cohete Ariane de la Agencia Espacial Europea-6_Media-Kit_english.pdf

El Nuevo Cohete Ariane de la Agencia Espacial Europea-6_Media-Kit_english.pdf

Collaborative Team Recommendation for Skilled Users: Objectives, Techniques, ...

Collaborative Team Recommendation for Skilled Users: Objectives, Techniques, ...

MCQ in Electrostatics. for class XII pptx

MCQ in Electrostatics. for class XII pptx

Testing the Son of God Hypothesis (Jesus Christ)

Testing the Son of God Hypothesis (Jesus Christ)

Modelling, Simulation, and Computer-aided Design in Computational, Evolutiona...

Modelling, Simulation, and Computer-aided Design in Computational, Evolutiona...

A slightly oblate dark matter halo revealed by a retrograde precessing Galact...

A slightly oblate dark matter halo revealed by a retrograde precessing Galact...

- 1. On the Axiom of Choice Flora Dellini Marco Natale Francesco Urso
- 2. Preliminary ›For every set S, a set U is a subset of S if, for every item in U, this item belongs to S too. ›For every set S, we define the set of the parts of S, P(S), as the set of all the possible subsets of S. Example: 𝑆 = 1,2,3 𝑃 𝑆 = {∅, 1 , 2 , 3 , 1,2 , 1,3 , 2,3 , {1,2,3}}
- 3. The Axiom of Choice (AC) › The Axiom of Choice is a statement about the existence of a certain kind of functions. › A choice function is a function which selects an item from a subset of a given set. › AC claims that, for every group of subsets of S, there exists a function of choice which selects a particular item from every given subset. ∀𝑆, ∀𝑈 ⊆ 𝑃 𝑆 ∅, ∃𝑓: 𝑈 → 𝑆 such that ∀𝑋 ∈ 𝑈, 𝑓(𝑋) ∈ 𝑋
- 4. AC: Examples with finite sets When a set is finite, everything is trivial. The existence of f is not disputable: we can actually show and build it! 𝑆 = 1,2,3,4,5 𝑈 = { 1 , 1,2,3 , 2,3 , 3,4,5 } ⊆ 𝑃(𝑆) 𝑓: 𝑈 ⊆ 𝑃(𝑆){∅} → 𝑆 𝑓 1 = 1 ∈ 1 𝑓 1,2,3 = 3 ∈ 1,2,3 𝑓 2,3 = 2 ∈ 2,3 𝑓 3,4,5 = 5 ∈ 3,4,5
- 5. AC: Examples of Infinite Sets Hilbert’s Shoes and Socks › Let’s suppose there is a shop with infinite pair of shoes, we want to built an infinite set containing a shoe for each pair. › A Turing machine (i.e. a personal computer) can choose between right or left shoe because it can distinguish them. For example we can build the set of all right shoes. › Can we do the same with infinite pair of socks?
- 6. AC: Examples of Infinite Sets Hilbert’s Shoes and Socks › A machine can not do it while a man could do. › The reason is: right and left shoes can be distinguished due to this feature. A man can do this, a machine can do it too. › It is not possible to choose right or left socks, because there are no such things as right or left socks! › As a consequence, in principle, a compuer can not build the wanted set.
- 7. AC: Examples of Infinite Sets Hilbert’s Shoes and Socks ›Could a man build a set from a single sock for each pair? ›Actually, it is impossible, because we would die before we can name all the items in the set. ›But is it possible in principle? How can we distinguish between the socks of a pair? ›We do this by choosing “this one”, without any criterion but our free will.
- 8. AC: Examples of Infinite Sets Hilbert’s Shoes and Socks ›As human beings, it is in our everyday experience that we can distinguish between two socks by calling «this one» or «that one». ›Is it admissible that in maths it is also possible to act in such a way? ›The answer is far from trivial!
- 9. The Way of Formalism › The mathematical concept of Set raised up in XIX century by Georg Cantor (1845-1918). › Cantor’s idea of Set was a “collection” of “objects” which satisfy certain properties (e.g. “the set of all odd numbers”, “the set of all the right shoes”). › Paradoxes arise from a “too free” use of the concept of “property”.
- 10. The Way of Formalism › Russell Paradoxes: the set of all the sets which don’t contain themselves. › The problem is in the semantic. › D. Hilbert’s “Formalism” school proposed the reduction of mathematics to a pure “formal game”. In this way, Mathematics would have been stripped of all its “human components”.
- 11. The Way of Formalism › Zermelo and Fraenkel, following Hilbert’s intuition, began to develop the Formal Set Theory (also known as ZF). › In according to the formalistic concept of mathematics, the semantic in ZF is “eliminated” reducing the concept of proprieties to pure syntactic formulas, computable in principle by a machine. › The nature of Sets is so implicitly defined by syntactic formulas.
- 12. The Way of Formalism ›The validity of a formula must be determined through “propositional calculus”, an absolutely formal procedure which can be, theoretically, implemented on an ideal machine. ›E.g. instead of saying “there is the empty set”, we shall write the following formula: ∃𝑦 ∀𝑥 (𝑥 ∉ 𝑦)
- 13. The Axioms of Zermelo-Fraenkel 1. Axioms describing implicitly the concept of Set (Regularity and Extensionality Axioms). 2. Axiom of Existence. The unique axiom of existence in ZF is the Axiom of Infinity, which asserts that there exists an infinite set. 3. Axioms of Individuation, which allow us to “individuate” (i.e. build) new sets starting from ones already known (Axiom of Power Set, Axiom of Union and Axiom of Replacement).
- 14. Is AC compatible with ZF? › Being compatible means that, if we add AC to ZF, we cannot deduce a theorem and its negation. › ZF claims to describe all mathematical universe: “…with regard to ZF it’s hard to conceive of any other model”. P. Cohen. › Because we would like to proceed in maths as we do with socks, that is by choosing items as we want to, the compatibility of AC with ZF is highly desirable.
- 15. ZF does not disprove AC “Inside only ZF, it’s not possible to prove that AC is false” (Gödel, 1938). Main steps of proof: 1. Gödel added another axiom to ZF (“every set is constructible”), obtaining the stronger theory ZFL. 2. Gödel proved that ZFL is consistent. In this stronger theory he proved that every set can be well-ordered, that is a demonstration of AC. So, ZFL → AC.
- 16. ZF does not disprove AC 3. If, by contradiction, AC is false in ZF, it has to be false also in ZFL. But we have just seen that AC is true in ZFL! So AC could not be disproved in ZF. ZF does not disprove AC! This does NOT mean that AC is true in ZF !
- 17. ZF does not imply AC In 1960 Cohen has completed Gödel’s demonstration about independence of AC from ZF. So ZF does not imply AC.
- 18. Independence of AC from ZF As a consequence, we can add or remove AC from ZF as we like. So, its presence is actually a preference of the mathematician who can want a “richer” or “poorer” theory.
- 19. Theorems we lose without AC • Every non empty Vectorial Space has a base – i.e. imagine that, in the classic Euclidean 3D space, you don’t have the 𝑖, 𝑗, and 𝑘 vectors you use to build every other vector. • Every field has an algebraic closure – i.e. imagine that you could not define the complex numbers
- 20. What does it mean? “Simply” that there are sets whose volume is not invariant under translation and rotation. Strange! Isn’t it? This is why some mathematicians worry about the Axiom of Choice Decomposition of a ball into four pieces which, properly rotated and traslated, yield two balls Counterintuitive effects of AC: Banach-Tarski Paradox
- 21. Counterintuitive effects of AC: Zermelo’s Lemma This statement is equivalent to the Axiom of Choice: Every set S can be well ordered As a consequence, we could «well order» ℝ - i.e. defining an order in ℝ such that every subset of ℝ has a minimum. This order relation is strongly counterintuitive, as it implies that sets like (0,1), without a minimum – 0 ∉ (0,1) do not exist.