Mathematics is defined as a system of logical processes grounded in axioms, theorems, and proofs, which provide a reliable framework for problem-solving. Key characteristics include consistency of rules, logical reasoning, and universality, making mathematics applicable across various disciplines. Ultimately, math serves as a powerful and objective tool for understanding and interpreting the world.

1. MATH IS A
SYSTEM
OF
LOGICAL
PROCESSE
PRESENTED BY GROUP 5

2. Learning
Outcomes
Explain the correlation of
math and logic
Today, you'll be able to:
Identify what is Logical
Processes
Discover the Components of
Mathematical Logic
Learn the definition of Math

3. What is
MATH?
• Mathematics was derived from the Greek
word “mathema”, which means “that
which is learnt”; while its modern Greek
equivalent is “mathaimo”.
• The encyclopedia defines Mathematics
as “the science of structure, order, and
relations that has evolved from
elemental practices of counting,
measuring, and describing the shapes
and characteristics of objects”.

4. MATHEMATICS
Mathematics, often perceived as a dry subject filled
with numbers and equations, is fundamentally a
system of logical processes. This means that it is
built upon a foundation of clear, consistent rules
and reasoning. Just as a well-constructed building
relies on a strong architectural blueprint,
mathematical concepts are rooted in logical
principles.

5. Key Components of
Mathematical Logic

6. Axioms:
These are fundamental
statements that are
assumed to be true
without proof. They serve
as the building blocks of
the mathematical system.
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EXAMPLE
In Euclidean geometry,
axioms such as "two
points determine a line"
and "all right angles are
congruent" are
foundational.
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7. Theorems and Lemmas:
These are statements that
can be proven to be true
based on the axioms and
definitions. Theorems are
major results, while lemmas
are smaller, intermediate
results that are often used
to prove larger theorems.
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Proofs:
A logical argument that
demonstrates the truth of
a theorem or lemma.
Proofs typically involve
deductive reasoning,
where conclusions are
drawn from established
facts or premises.
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8. Characteristics:
• Consistency of Rules - Math follows consistent
rules and principles, such as addition, subtraction,
multiplication, and division. To deliver reliable and
consistent results.
• Logical Reasoning - Math relies on logical
reasoning to generate new knowledge from existing
facts. It uses deductive reasoning. Ensures that the
conclusions are logically sound and rooted in
established truths.

9. • Proofs and Validity - Mathematical proofs are
logical arguments that confirm the truth of a
statement. It logically follow from accepted
premises or truths, ensuring that mathematical
statements are reliable and valid.
• Problem Solving - Math offers a systematic
approach to problem-solving. By using logical steps
and established rules, mathematicians can
decompose complex problems into simpler parts,
leading to precise and accurate solutions.

10. • Universality and Objectivity - The logical nature of
math makes it universal and objective.
Mathematical principles and conclusions are
consistent, regardless of context or perspective,
making math a powerful tool across disciplines like
science, engineering, and economics.

11. CONCLUSIO
N:
Math is a system of logical processes
because it is founded on basic
principles, adheres to consistent rules,
utilizes structured reasoning,
validates statements through proofs,
and provides objective solutions to
problems. This logical framework
makes math a reliable and universal
language for understanding the
world.

12. THANK YOU FOR
LISTENING!
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