Two quantities are equal if they are, in some well-defined sense, equivalent. Robert Recorde introduced the equals sign in The Whetstone
of Witte in 1557 (History of Mathematics Project). Equality of quantities 
and 
is written 
.
Equality of multiple expressions is commonly denoted
 |  |  |
(1)
|
 |  |  |
(2)
|
which is equivalent to 
.
Equality is transitive, so if 
and 
,
then it is also true that 
.
A symbol with three horizontal line segments (
) resembling the equals sign is used to denote both equality
by definition (e.g., 
means 
is defined
to be equal to 
)
and congruence (e.g., 
means 13 divided by 12 leaves a remainder
of 1--a fact known to all readers of analog clocks).
Given an expression involving known constants, integration in finite terms, computation of limits, etc., the constant problem asks to
determine if the expression is equal to zero (or, equivalently, if the equality 
holds, since this is equivalent to
). In general, this is a very difficult
(and unsolved) problem.
Equal is implemented in the Wolfram Language as Equal[A, B, ...], or A == B == ....
Equalities that the Wolfram Language cannot establish "out of the box" include
(1+Sqrt[5])/2 == GoldenRatio (1+E)^2 == 1+2E+E^2
