Difference between revisions of "Inequality symbol"

Revision as of 17:22, 12 November 2006

There are four symbols conventionally used to represent the notion of inequality.

If $a$ and $b$ are real numbers we write:

$a > b$ to mean that $a$ is strictly greater than $b$ (that is, $a$ cannot equal $b$ ).

$a \geq b$ to mean that $a$ is greater than or equal to (equivalently, "at least as large as") $b$ .

$a < b$ to mean that $a$ is strictly less than $b$

$a \leq b$ to mean that $a$ is less than or equal to $b$ .

We use a slash through an inequality symbol to represent that the given inequality does not hold. Thus for real numbers $a$ and $b$ ,

$a \not > b$ if and only if $a \leq b$
$a \not \geq b$ if and only if $a < b$
$a \not < b$ if and only if $a \geq b$
$a \not \leq b$ if and only if $a > b$
$\displaystyle a \neq b$ if and only if $a > b$ or $a < b$

These symbols are also frequently used to represent the order relation in a partially ordered set. Note that in this more general setting, it is not necessarily true that $a \not > b \Longleftrightarrow a \leq b$ , because it is also possible that $a$ and $b$ could be incomparable.

@@ Line 19: / Line 19: @@
 * <math>a \not \leq b</math> if and only if <math>a > b</math>
 * <math>\displaystyle a \neq b</math> if and only if <math>a > b</math> or <math>a < b</math>
+These symbols are also frequently used to represent the order [[relation]] in a [[partially ordered set]].  Note that in this more general setting, it is ''not'' necessarily true that <math>a \not > b \Longleftrightarrow a \leq b</math>, because it is also possible that <math>a</math> and <math>b</math> could be incomparable.

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Difference between revisions of "Inequality symbol"

Revision as of 17:22, 12 November 2006