Integer
Elementary
An integer is a whole number or the negative of a whole number:
\[\dots, -3, -2, -1, 0, 1, 2, 3, \dots\]
Undergraduate
An integer is an element of $\mathbb{Z}$, which can be constructed from the natural numbers as equivalence classes of pairs $(a, b)$ of natural numbers, where $(a, b)$ represents $a - b$ and $(a, b) \sim (c, d)$ if $a + d = b + c$.
Examples
Non-examples
Things that may be mistaken for examples.
-
$\pi$
Elementary
$\pi$ is irrational, not an integer, and not algebraic, because it is transcendental.
- $\sqrt{2}$ High school