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: $\N$, $\Z$, $\Q$, $\R$:
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: $\N$, $\Z$, $\Q$, $\R$:
The $\LaTeX$ code for \(\ge\) is \ge or \geq.
The $\LaTeX$ code for \(\geqslant\) is \geqslant .
Negation
- $\not >$, $\not <$, $\not \ge$, $\not \le$
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 =.
Not Equal To
- $\ne$
Not Equal To.
A binary relation on a pair of objects:
- $a \ne b$ if and only if $a$ is not equal to $b$
Its $\LaTeX$ code is \ne or \neq.
Sources
- 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Inequalities
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols