# Symbols:Inequalities

## Symbols

The inequality symbols are symbols denoting relations expressing inequalities on (usually) the sets of numbers: $\N$, $\Z$, $\Q$, $\R$.

### Less Than

$<$

Less than.

A binary relation expressing the usual ordering on one of the sets of numbers: $\N$, $\Z$, $\Q$, $\R$:

$a < b \iff b - a$ is strictly positive

Its $\LaTeX$ code is < .

### Greater Than

$>$

Greater than.

A binary relation expressing the usual ordering on one of the sets of numbers: $\N$, $\Z$, $\Q$, $\R$:

$a > b \iff a - b$ is strictly positive

Its $\LaTeX$ code is > .

### Less Than or Equal To

$\le$ or $\leqslant$

Less than or equal to.

A binary relation expressing the usual ordering on one of the sets of numbers: $\N$, $\Z$, $\Q$, $\R$:

$a \le b \iff b - a$ is positive or zero.

The $\LaTeX$ code for $\le$ is \le  or \leq.

The $\LaTeX$ code for $\leqslant$ is \leqslant .

### Greater Than or Equal To

$\ge$ or $\geqslant$

Greater than or equal to.

A binary relation expressing the usual ordering on one of the sets of numbers: $\N$, $\Z$, $\Q$, $\R$:

$a \ge b \iff a - b$ is positive or zero.

The $\LaTeX$ code for $\ge$ is \ge  or \geq.

The $\LaTeX$ code for $\geqslant$ is \geqslant .

## Negation

$\ne, \not >, \not <, \not \ge, \not \le$

The above symbols all mean the opposite of the non struck through version of the symbol.

For example, $x \ne y$ means that $x$ is not equal to $y$.

The $\LaTeX$ code for negation is \not followed by the code for whatever symbol you want to negate.

For example: \not \ge will render $\not \ge$.

Note that some of the above relations also have their own $\LaTeX$ commands for their negations, for example \ne or \neq for \not =.