# Equality

## Equality

Relationship between two quantities of the same value or between two representations of the same mathematical object.

An equality can be either true, either false. It cannot be true and false at the same time. The truth or untruth property of an equality is called its truth value.

### Notation

• The relationship of equality is noted using the symbol “=” which is read as “is equal to”.
• This symbol can only be used between numbers, numerical variables, vectors, matrices, or sets.
• 7 = 5 + 2 is a true equality, but 17 = 1 + 7  is a false equality.

### Example

• The relationship 12 + 21 = 33 is read as “twelve plus twenty-one is equal to thirty-three”.
• E = {1, 2, 3} means that the letter E represents the set containing the elements 1, 2, and 3.
• ℜ = {(1, 2), (3, 4), (7, 6)} means that the letter ℜ is used here to represent the relationship (or the set) containing the ordered pairs (1, 2), (3, 4), and (7, 6).

### Didactical Note

The symbol “=” is attributed to Robert Recorde, a Welsh mathematician and doctor. He used it in the first book about algebra written in English, The Whetstone of witte in 1557. In its initial version, the two lines were much longer. Surprisingly, the symbol did not appear again until 1631 when it was used by William Oughtred (1574-1660).