MATHS Equations and definitions

This note is a compact symbol guide for the top-level maths folder. Local subject notes give the full detail.

Logic and sets

• $x\in A$: $x$ is an element of Set $A$.
• $A\subseteq B$: every element of $A$ is also in $B$.
• $A\cup B$, $A\cap B$, $A\setminus B$: union, intersection, and difference.
• $A\times B=\{(a,b):a\in A,b\in B\}$: Cartesian product.
• arnothing: the empty set.

Functions

• $f:X\to Y$: a Function with Domain $X$ and codomain $Y$.
• $f(x)$: the output assigned to input $x$.
• $\mathrm{im}(f)=\{f(x):x\in X\}$: image/range.
• $f^{-1}$: inverse function, when it exists as a function; see Inverse functions.

Common number sets

• $\mathbb{N},\mathbb{Z},\mathbb{Q},\mathbb{R},\mathbb{C}$: natural, integer, rational, real, and complex numbers; see Number sets.
• $[a,b]$, $(a,b)$, $[a,b)$: closed/open/half-open intervals.

Calculus symbols

• $\frac{dy}{dx}$ or $f^{\prime }(x)$: Derivative.
• ${\int }_a^{b}f(x)dx$: definite Integral.
• $abla$: Del operator ∇, used for gradient, divergence, and curl.

Units matter when applying these to physics: a derivative of position with respect to time has units of Metre per Second.