Frequently used symbols#
Symbol |
Meaning |
|---|---|
\(\varepsilon\) |
epsilon |
\(\delta\) |
delta |
\(\subseteq\) |
subset of |
\(\in\) |
element of |
\(\notin\) |
not an element of |
\(\forall\) |
for all |
\(\exists\) |
there exists |
s.t. |
such that |
\(:=\) |
defined to be equal to |
\(\mathbb{N} := \{1,2,\ldots\}\) |
the natural numbers |
\(\mathbb{N}_0 := \mathbb{N}\cup\{0\}\) |
the non-negative integers |
\(\mathbb{Z} := \{0,\pm 1,\pm 2,...\}\) |
the integers |
\(\mathbb{Q} := \left\{\frac{p}{q}:p\in\mathbb{Z},q\in\mathbb{N}\right\}\) |
the rationals |
\(\mathbb{R}\) |
the reals |
\(f:X\to\mathbb{R}\) |
a function \(f\) from \(X\) to \(\mathbb{R}\) |
\(x\mapsto f(x)\) |
\(x\) maps to \(f(x)\) |
\(\text{Dom}(f)\) |
domain of \(f\) |
\(\text{Range}(f)\) |
range of \(f\) |
\([a,b]:=\{x\in\mathbb{R}:a\leq x\leq b\}\) |
closed interval from \(a\) to \(b\) |
\((a,b):=\{x\in\mathbb{R}:a<x<b\}\) |
open interval from \(a\) to \(b\) |
\([a,b)\) and \((a,b]\) |
half-open intervals |
\(\mathbb{1}_S\) |
indicator function for a set \(S\subseteq\mathbb{R}\). See Example 2.4 |
\(U(f,P)\) |
upper sum of \(f\) with respect to \(P\). See Definition 6.1 |
\(L(f,P)\) |
lower sum of \(f\) with respect to \(P\). See Definition 6.1 |
\(U(f)\) |
upper (Riemann) integral of \(f\). See Definition 6.3 |
\(L(f)\) |
lower (Riemann) integral of \(f\). See Definition 6.3 |