Symbols:General

Equals

$x = y$ means $x$ is the same object as $y$, and is read $x$ equals $y$, or $x$ is equal to $y$.

$x \ne y$ means $x$ is not the same object as $y$, and is read $x$ is not equal to $y$.

The expression:

$a = b$

means:

$a$ and $b$ are names for the same object.

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

The $\LaTeX$ code for $\ne$ is \ne or (deprecated) \neq.

Negation

$\not=, \not>, \not<, \not \ge, \not \le, \not \in, \not \exists, \not \subseteq, \not \subset, \not \supseteq, \not \supset$

Negation. The above symbols all mean the opposite of the non struck through version of the symbol. For example, $x \not\in S$ means that $x$ is not an element of $S$. The slash through a symbol ($/$ ) can be used to reverse the meaning of essentially any mathematical symbol (especially relations), although it is used most frequently with those listed above. Note that $\not \subsetneq$ and $\not \supsetneq$ can be confusing due to the strike through of the symbol as a whole and the strike through of the equivalence bar on the bottom, and hence should likely be avoided.

The $\LaTeX$ code for negation is \not followed by the code for whatever symbol you want to negate. For example, \not \in will render $\not\in$

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

See Arithmetic and Algebra and Set Operations and Relations for the definitions of the symbols above.

Prime

$x'$

The symbol $'$ is a general indicator of another version of or another type of where the specific version or type that is being described is to be defined.

The symbol $x'$ should technically be voiced x prime, although colloquially referred to as some variant of x dash or x tick or whatever can be devised by the ingenuity of the reader.

The $\LaTeX$ code for $x'$ is x' or (the verbose version) x^{\prime}.