Question

What is the FUNDAMENTAL theorem of MATHEMATICS?

Answer 1

Answer:

In mathematics, the fundamental theorem of a field is the theorem which is considered to be the most central and the important one to that field.[1] As such, its naming is not necessarily based on the difficulty of its proofs, or how often it is used.[2]

For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus, which are two distinct branches of calculus that were not previously obviously related. On the other hand, being "fundamental" does not necessarily mean that it is the most basic result. For example, the proof of the fundamental theorem of arithmetic requires Euclid's lemma,[3] which in turn requires Bézout's identity.[4]

The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory.

The mathematical literature sometimes refers to the fundamental lemma of a field. The term lemma is conventionally used to denote a proven proposition which is used as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. The fundamental lemma of a field is often the same as the fundamental theorem of that field (such as the case with the fundamental lemma of the Langlands program[5]), though the two need not to be always identical

Answer 2

Answer:

Fundamental theorem of arithmetic states that every composite number can be expressed as a product of primes,and this prime factorization is unique apart from the prime factors occur