# Monoidal Identity¶

The monoidal identity is the identity value for a particular monoid. A monoid must have an identity value and an associative binary operation. The identity value m is a value which makes no change to any other value n in that monoid, when n is combined with m using that binary operation.

1 is the monoidal identity for natural numbers under multiplication. 1 \cdot n = n \cdot 1 = n. 0 is the monoidal identity for natural numbers under addition. 0 + n = n + 0 = n

## Backlinks¶

- Monoid
- A monoid is an algebraic structure with an identity value and an associative binary operation.

- Product Type
- Product types have a monoidal identity of Unit. |Unit| = 1.

- Sum Type
- The monoidal identity of the sum operation is the void type, as |Void| = 0.