Difference between revisions of "Inequality"

Revision as of 21:59, May 9, 2011

An inequality is a mathematical expression concerning the relative size of two terms.

These come in five kinds;

An expression in which the left hand side is strictly greater than the right, denoted: $>$
An expression in which the left hand side is greater than or equal than the right, denoted: $\geq$
An expression in which the left hand side is strictly less than the right, denoted: $<$
An expression in which the left hand side is greater than or equal than the right, denoted: $\leq$
An expression in which the left hand side is not equal to the right, but no further information is implied, denoted: $\neq$

For example, 4 is greater than 3, so either;

4>3

3<4

are true statements.

The inequalities are widely used in more advanced mathematics for example the cosine function is always between -1 and 1 inclusive so you can write:

$-1\leq \cos x\leq 1\;\forall x\in \mathbb {R}$ .

This gives the function's bounds. ' $\forall x\in \mathbb {R}$ ' means that the preceding inequality is true for all real values of $x$ .

@@ Line 16: / Line 16: @@
 are true statements.
-The inequalities are widely used in more advanced mathematics for example the [[cosine function]] is always between -1 and 1 inclusive so you can write;
+The inequalities are widely used in more advanced mathematics for example the [[cosine function]] is always between -1 and 1 inclusive so you can write:
 <math>-1\leq\cos x\leq1\; \forall x\in\mathbb{R}</math>.
-This gives the function [[bounds]].
+This gives the function's [[bounds]]. '<math>\forall x\in\mathbb{R}</math>' means that the preceding inequality is true for all [[Real numbers|real]] values of <math>x</math>.
 ==See also==
 *[[Equation]]
 [[Category:mathematics]]