In mathematics, an inequation is a statement that two objects or expressions are not the same, or do not represent the same value. This relation is written with a crossed-out equal sign, like
In programming languages and electronic communications, the notations
x != yx /= yx <> y
and others, are used instead.
Inequations should not be confused with mathematical inequalities, which express numerical relations such as 3 < 5 (3 is less than 5). In a linearly ordered set, any inequation implies an inequality: if x ≠ y then x < y or x > y by the trichotomy law.
Verbally it may be spoken as "does not equal." For example the written inequation "3 ≠ 2" would be spoken as "Three does not equal two."
Contents |
Properties
Some useful properties of inequations in algebra are:
- Any quantity can be added to both sides.
- Any quantity can be subtracted from both sides.
- Both sides can be multiplied by any nonzero quantity.
- Both sides can be divided by any nonzero quantity.
- Generally, any injective function can be applied to both sides.
Property (5) is somewhat of a tautology, since injective functions may be defined as functions that always preserve inequations.
If a function that is not injective is applied to both sides of an inequation, the resulting statement may be false. For an extreme example, if f is a constant function, such as multiplication by zero, then the statement "f(x) ≠ f(y)" is always false. This consideration explains why one must use a nonzero quantity in property (3) above.
Systems of inequations
A system of inequations can be represented by a set of n variables {x1, x2, … xn} and a set of inequations involving some (possibly empty) subset of all pairs of variables (xi, xj) for i ≠ j. The idea is analogous to a system of equations, since any valid solution must simultaneously satisfy all of the inequations in the system. For example if n = 2 the system is represented by a single inequation
See also
| Look up inequation in Wiktionary, the free dictionary. |
References
| This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be and removed. (October 2008) |
Categories: Elementary algebra
|
Tom_Pascal
hu, 02 Apr 2009 15:41:46 GM
inequation. avec les axes. ... re : . inequation. avec les axes #msg2371863 Poste le 03-04-09 a 20:39. Poste par Profil nessi38 nessi38. Merci de m'avoir aider ela ma aider pour le cotrole que j'ai eu se matin qui ma parru tres facile ...
