Equal
Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities 
and 
is written 
. Equal is implemented in the Wolfram
Language as Equal[A,
B, ...], or A==B==....
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.
Equalities that the Wolfram Language cannot establish "out of the box" include
(1+Sqrt[5])/2 == GoldenRatio (1+E)^2 == 1+2E+E^2
Contact the MathWorld Team
equal
