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~An axiom is a finite statement that is accepted to be true without proof.
~A starting point for deducing and inferring other (theory dependent) truths.
To demand or claim without proof
~System of natural numbers
~Accessibly infinite formal system.
Different beliefs in Mathematics can lead to useful real-life applications, previously unthought of.
Axioms must be consistent to base assumptions in mathematics.
~Everything that is, is.
~What isn’t not is more like is than is not.
~What is not false is sometimes true.
~What is not true is sometimes false.
~What is always sometimes true is at least a little bit true.
~What is always sometimes false is at least a little bit false.
~If two lines intersect, then they intersect at exactly one point.
~All planets revolve around the sun.
~The earth turns 360 degrees everyday.
~Probability lies between 0 & 1
~A theorem is a theoretical proposition, statement, or formula proved by a chain of reasoning; a truth established by means of accepted truths.
Pythagorean
Theorem
Pythagorean equation: a2 + b2 = c2. Pythagorean theorem states that the area of the square formed by the longest side of the right triangle (the hypotenuse) is equal to the sum of the area of the squares formed by the other two sides of the right triangle:
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski.
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.
An axiom is a statement that is considered to be true, based on logic; however, it cannot be proven or demonstrated because it is simply considered as self-evident. ... A theorem, by definition, is a statement proven based on axioms, other theorems, and some set of logical connectives.