# Fundamental Theorems - Fundamental Theorem Of Algebra, Fundamental Theorem Of Calculus - Fundamental theorem of arithmetic

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subject branch prime

A fundamental **theorem** is a statement or proposition so named because it has consequences for the subject matter that are difficult to overestimate. Put another way, a fundamental theorem lies at the very heart of the subject. Mathematicians have designated one theorem in each main branch as fundamental to that branch.

The fundamental theorem of **arithmetic** states that every number can be written as the product of **prime numbers** in essentially one way. For example, there are no prime factors of 30 other than 2, 3, and 5. You cannot **factor** 30 so that it contains 2s and a 7 or some other combination.

## Additional Topics

The fundamental theorem of calculus asserts that differentiation and integration are inverse operations, a fact that is not at all obvious, and was not immediately apparent to the inventors of calculus either. The derivative of a function is a measure of the rate of change of the function. On the other hand, the integral of a function from a to b is a measure of the area under the graph of that fu…

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