# Theorem

## Characteristics Of A Theorem

The initial premises on which all theorems are based are called axioms. An axiom, or **postulate**, is a basic fact which is not subject to formal proof. For example, the statement that there is an infinite number of even **integers** is a simple axiom. Another is that two points can be joined to form a line. When developing a theorem, mathematicians choose axioms, which seem most reliable based on their experience. In this way, they can be certain that the theorems are proved as near to the truth as possible. However, absolute truth is not possible because axioms are not absolutely true.

To develop theorems, mathematicians also use definitions. Definitions state the meaning of lengthy concepts in a single word or phrase. In this way, when we talk about a figure made by the set of all points which are a certain **distance** from a central point, we can just use the word *circle*.

See also Symbolic logic.

## Resources

### Books

Dunham, William. *Journey Through Genius.* New York: Wiley, 1990.

Kline, Morris. *Mathematics for the Nonmathematician.* New York: Dover, 1967.

Lloyd, G.E R. *Early Greek Science: Thales to Aristotle.* New York: W. W. Norton, 1970.

Newman, James R., ed. *The World of Mathematics.* New York: Simon and Schuster, 1956.

Paulos, John Allen. *Beyond Numeracy.* New York: Knopf, 1991.

Perry Romanowski

## Additional topics

Science EncyclopediaScience & Philosophy: *Thallophyta* to *Toxicology*Theorem - Historical Background, Characteristics Of A Theorem