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

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

See also

Congruence, Constant Problem, Defined, Different, Equality, Equivalence Relation, Equivalent, Hidden Zero, Isomorphism, Transitive, Unequal Explore this topic in the MathWorld classroom

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References

History of Mathematics Project. "Recorde's Whetstone of Witte." Wikimedia Commons image. https://www.history-of-mathematics.org/artifacts/recordes-whetstone-of-witte.

Referenced on Wolfram|Alpha

Equal

Cite this as:

Weisstein, Eric W. "Equal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Equal.html

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