Inequation
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In mathematics, an inequation is a statement that two objects or expressions are not the same, or do not represent the same value.[1] This relation is written with a crossed-out equal sign ("≠", Unicode 2260, HTML ≠ or ≠) as in
Verbally it may be spoken as "does not equal," or "is unequal to." In programming languages and electronic communications, the notations
x != yx /= yx <> y
and others, are used instead.
Some sources[2] use the term inequation synonymously with inequality. Others[3] include ≠ as a type of inequality. In a linearly ordered set, any inequation implies an inequality: if x ≠ y then x < y or x > y by the trichotomy law.
[edit] Properties
Some useful properties of inequations in algebra are:
- Any quantity can be added or subtracted to both sides.
- Both sides can be multiplied or divided by any nonzero quantity. When multiplying or dividing both sides by a negative number, a "<" sign must be changed to a ">" sign and vice-versa in order to retain the truth value. For example 4 < 5 (true), (-1)(4)>(-1)(5), -4 > -5 (still true).
- Generally, any injective function can be applied to both sides. (This is something of a tautology, since injective functions may be defined as functions that always preserve inequations.)
[edit] See also
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Look up inequation in Wiktionary, the free dictionary. |
[edit] References
- ^ Weisstein, Eric W., "Inequation" from MathWorld.
- ^ For example Sinha, K.C.. A Text Book of Mathematics XI. Rastogi. ISBN 8171339123.
- ^ For example Hazewinkel, Michiel, ed. (2001), "Inequality", Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=I/i050790
