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Gödel's theorem states that it is impossible to make a complete set of mathematical axioms that can explain every truth about arithmetics.
This means that no matter how you define the fundamental axioms of mathematics, there have to be certain statements that are true within mathematics that can not be formally proved by using the fundamental axioms. This theorem pretty much shattered the mathematician's dream of describing all of mathematics within a framework of a limited number of logical axioms. Nevertheless, the axiomatic Zermelo-Frankel set theory is able to explain all of the known mathematics from fundamental axioms, but philosophically it is still not a complete theory.
Although the theorem is extremely complicated, it can be understood by anybody with a basic mathematical knowledge. This link shows a version of the proof:
http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/godel.html
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Does Godels Incompleteness Theorem imply axioms do not exist?
No, not at all. The Incompleteness Theorem is more like, that there will always be things that can't be proven. Further, it is impossible to find a complete and consistent set of axioms, meaning you can find an incomplete set of axioms, or an inconsistent set of axioms, but not both a complete and consistent set.
The Pythagorean theorem belongs to which science field?
Plane geometry.
Why is mathematics a proximate science?
Mathematics is a proximate science because 1+1=2 and that is definite.It's a fact and proven by theorem therefore it is academically accepted without furthermore questioning.
What is norton's theorem?
Norton's theorem is the current equivalent of Thevenin's theorem.
How do you solve a remainder theorem?
You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
