# Definition:Equals

## Definition

The symbol $=$ means equals.

$x = y$ means $x$ is the same object as $y$, and is read $x$ equals $y$, or $x$ is equal to $y$.
$x \ne y$ means $x$ is not the same object as $y$, and is read $x$ is not equal to $y$.

The expression:

$a = b$

means:

$a$ and $b$ are names for the same object.

### Equality

The word equality is the noun derived from the verb equals.

## Note on Terminology

Two objects being equal is not necessarily the same as two objects being congruent.

This distinction is often not made.

When such a difference is important the symbol $=$ may be used for equals and $\cong$ for congruent.

## Historical Note

The equals sign was introduced by Robert Recorde in his $1557$ work The Whetstone of Witte.

Placing two long hyphens together, one above the other, he wrote:

To avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a paire of paralleles, or gemowe lines of one lengthe: $= \!\!\! = \!\!\! = \!\!\! = \!\!\! = \!\!\! = \!\!\! =$, bicause noe .2. thynges, can be moare equalle.

The word gemowe comes from the Latin geminus meaning twin.

François Viète used the symbol $\sim$, while René Descartes used $\propto$.

Both were in due course supplanted by $=$, a shortened and hence more efficient version of Recorde's invention.

It is suggested by some sources that this was mainly through the influence of Leibniz.