Introduction
1. Two proofs:
Pythagorean Theorem
is an irrational number
Fermat’s Last Theorem
Poincare Conjecture
2. Fundamental Theorem of Arithmetic:
Every
positive integer n can be written as
the product of prime numbers.
Precise statement of the Fundamental Theorem of Arithmetic
3. There exists infinitely many primes.
4.
is
an irrational number. Proof
5.
6.
Inductive Reasoning: Arriving
at conclusion based on specific examples or observations. Given the premises, the conclusion is likely
to be true but not certain.
Deductive Reasoning: Forming a conclusion that is based on general
principles or axioms. If the premises
are true then the conclusion is guaranteed to follow.