Symbols:Inequalities

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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

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

Negation.

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 =.


Sources