Inequation

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In mathematics, an inequation is a statement that an inequality holds between two values.[1] It is usually written in the form of a pair of expressions denoting the values in question, with a relational sign between them indicating the specific inequality relation. Some examples of inequations are:

a < b,\,
x+y+z \leq 1,\,
n > 1,\,
x \neq 0.\,

Some authors apply the term only to inequations in which the inequality relation is, specifically, not-equal-to (≠).[2]

Chains of inequations

A shorthand notation is used for the conjunction of several inequations involving common expressions, by chaining them together. For example, the chain

0 \leq a < b \leq 1\,

is shorthand for

0 \leq a~\mathrm{and}~a< b~\mathrm{and}~b\leq 1.\,

See also

Look up inequation in Wiktionary, the free dictionary.

References

  1. ^ Thomas H. Sidebotham (2002). The A to Z of Mathematics: A Basic Guide. John Wiley and Sons. p. 252. ISBN 0-471-15045-2.
  2. ^ Weisstein, Eric W., "Inequation" from MathWorld.