The following notations are the standard notations I use in mathematics.
Set theoretic notations: union : \(A \sqcup B\); intersection : \(A\sqcap B\); disjoint union is denoted: \(A \mho B\) (\mho in TeX settings):\( \mho_{i = 1}^{n} A_i \) ;
Orders: less than or equal to: \( a \leqslant b \); greater than or equal to: \(a \geqslant b\);
Standard sets for numbers: \(\mathbb{N} = \{0, 1, 2, \dots\} \); \( \mathbb{Z}^{+}\): positive integers, i.e. \(x\in \mathbb{Z}, x > 0\); \(\mathbb{R}^{+}\): positive reals,
i.e. the set of reals \(x>0\);
Topology : \(B_{r}(x)\): open ball of radius \(r>0\) around \(x\); \( B_{r]}(x) \): closed ball of radius \(r>0\) around \(x\);
Measure and Integration : \(\mu[A] \): the measure of the measurable set \(A\); if \(T: (X, \mu) \to Y\), \(T_{\#}\mu \) is the measure image of
\(\mu\), i.e. its pushforward, defined as \(T_{\#}\mu[B] = \mu[T^{-1}(B)]\). A transformation \( T: (X, \mu) \to (Y, \nu)\) is said to be measure preserving if \(\nu = T_{\#}\mu\).
Abstract Algebra: Group of units \(U(R) \) where \(R\) is a ring; zero divisors \(ZD(R)\); normal subgroup \(H \trianglelefteq G\);