# fundamental theorem

## English[edit]

### Noun[edit]

**fundamental theorem** (*plural* **fundamental theorems**)

- (chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field.
**1994**, Joseph E. Stiglitz,*Whither Socialism?*, The MIT Press, page 27,- In this and the next chapter I return to the
**fundamental theorems**of welfare economics. In this chapter I argue that the first**fundamental theorem**of welfare economics—asserting the efficiency of competitive economics—is fundamentally flawed.

- In this and the next chapter I return to the
**2010**, Vasily E. Tarasov,*Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media*, Springer, page 247,- The first
**fundamental theorem**of calculus states that the differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is obtained […] .

- The first
**2012**, Joseph L. Taylor,*Foundations of Analysis*, American Mathematical Society, page 114,- There are two
**fundamental theorems**of calculus. Both relate differentiation to integration. In most calculus courses, the Second**Fundamental Theorem**is usually proved first and then used to prove the First**Fundamental Theorem**. Unfortunately, this results in a First**Fundamental Theorem**that is weaker than it could be.

- There are two

#### Usage notes[edit]

In usages outside mathematics proper, some * fundamental theorems* may still be expressed mathematically and even "proven" in the context of an accepted mathematical model.