$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
 $$\bot$$ is perpendicular to $$\emptyset$$ The empty set - a set containing no elements $$<$$ is less than $$>$$ is greater than $$\geq$$ is greater than or equal to $$\leq$$ is less than or equal to $$!$$ Fractorial $$\rightarrow$$ which implies that $$\leftrightarrow$$ if and only if $$f(x)$$ A function or relation in the variable $$x$$ $$(a,b)$$ An ordered pair. This notation can be used in the context of sets describing, the set consisting of all real numbers which lies between $$a$$ and $$b$$ whenever $$a$$ and $$b$$ are real numbers. This notation may also be used to denote the coordinates of a point in two dimensions. $$\in$$ is an element of $$\notin$$ is not an element of $$\subseteq$$ is a subset of $$\subset$$ is a proper subset of $$\cup$$ Union $$\cap$$ Intersection $$|a|$$ The absolute value of $$a$$ $$\neq$$ is not equal to acute angle An angle which has measure between $$0^\circ$$ and $$90^\circ$$. obtuse angle An angle which has measure between $$90^\circ$$ and $$180^\circ$$. hypotenuse The side in a right angle which is opposite to the right angle. $$\overline{AB}$$ The length of the line segment $$AB$$ $$\approx$$ is approximately equal to $$\sim$$ is equivalent to $$\ln(x)$$ Natural logarithm of $$x$$. The logarithm of $$x$$ to the base $$e$$. $$\log(x)$$ Common logarithm of $$x$$. The logarithm of $$x$$ to the base $$10$$. $$\log_a(x)$$ Logarith of $$x$$ to the base $$a$$, $$a \ne 1$$, $$a>1$$ . $$\infty$$ Infinity $$\alpha$$ The greek letter - alpha $$\beta$$ The greek letter - beta $$dom(f)$$ The domain of the relation $$f$$ $$rg(f)$$ The range of the relation $$f$$ $$\mathbb{R}$$ The set of all real numbers $$\mathbb{Q}$$ The set of all rational numbers $$\mathbb{Q^c}$$ The set of all irrational numbers $$\mathbb{N}$$ The set of all natural numbers $$\mathbb{Z}$$ The set of all integers