Zero (the number)

Definition · applies to numbers · also called $0$

Elementary

Consider a box that could contain some items. If there are no items in the box, then number of items is zero.

Undergraduate

The number zero is the additive identity of real and complex numbers.

Examples

Examples

• $0$ Elementary

Non-examples

Things that may be mistaken for examples.

• $(0, 0) \in \reals^2$, for vector addition High school
  $(0, 0)$ is not the number zero, because it is a vector.
• $2$, for $f(x) = x^2 - 4$ High school
  $2$ is not the number zero.

Properties

• $a + 0 = a$ and $a \cdot 0 = 0$ for every number $a$. Division by $0$ is undefined.

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