Math Project
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Math Project Math Project Presentation Transcript

  • Real Numbers
  • Real Numbers By Kristle Wilson
  • By Kristle Wilson
  • What are Natural Numbers
  • What are Natural Numbers In math, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century.
  • What are Natural Numbers In math, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century. Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of
  • What are Natural Numbers Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of
  • What are Natural Numbers
  • What Is a Whole Number
  • The term whole number does not have a Real definition. Various authors use it in one of the following senses:
  • The term whole number does not have a Real definition. Various authors use it in one of the following senses: ■ the nonnegative integers (0, 1, 2, 3, ...)
  • The term whole number does not have a Real definition. Various authors use it in one of the following senses: ■ the nonnegative integers (0, 1, 2, 3, ...) ■ the positive integers (1, 2, 3, ...)
  • The term whole number does not have a Real definition. Various authors use it in one of the following senses: ■ the nonnegative integers (0, 1, 2, 3, ...) ■ the positive integers (1, 2, 3, ...) ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
  • ■ the nonnegative integers (0, 1, 2, 3, ...) ■ the positive integers (1, 2, 3, ...) ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
  • ■ the positive integers (1, 2, 3, ...) ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
  • ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
  • What Are Integers
  • S: (n) integer, whole number (any of the natural numbers (positive or negative) or zero) "an integer is a number that is not a fraction"
  • What is A real Number
  • In Math the real numbers may be described informally in several different ways. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an infinitely long number line.
  • Rational Numbers
  • In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient).
  • In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient). Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0.
  • In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient). Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0. The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.
  • In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient). Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0. The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
  • Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0. The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
  • The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
  • A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
  • What Is A Irrational
  • A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational.
  • A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational. In abstract algebra, the rational numbers form a field. This is the archetypical field of characteristic zero, and is the field of fractions for the ring of integers. Finite extensions of are called algebraic number fields, and the algebraic closure of is the field of algebraic numbers.
  • A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational. In abstract algebra, the rational numbers form a field. This is the archetypical field of characteristic zero, and is the field of fractions for the ring of integers. Finite extensions of are called algebraic number fields, and the algebraic closure of is the field of algebraic numbers.
  • A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational. In abstract algebra, the rational numbers form a field. This is the archetypical field of characteristic zero, and is the field of fractions for the ring of integers. Finite extensions of are called algebraic number fields, and the algebraic closure of is the field of algebraic numbers.
  • In abstract algebra, the rational numbers form a field. This is the archetypical field of characteristic zero, and is the field of fractions for the ring of integers. Finite extensions of are called algebraic number fields, and the algebraic closure of is the field of algebraic numbers.
  • Chart Irrational Rational Integers Whole Natural
  • Bibliography
  • Bibliography
  • Bibliography http://en.wikipedia.org/wiki/Natural_number
  • Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number
  • Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer
  • Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number
  • Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
  • Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
  • Bibliography http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
  • Bibliography http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
  • Bibliography http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
  • Bibliography http://en.wikipedia.org/wiki/Rational_numbers
  • Bibliography
  • Bibliography