abstractmath.org 2.0
help with abstract math


Produced by Charles Wells   Revised 2015-06-22
Introduction to this website     website TOC     website index     blog     head of Symbolic Language chapter

Contents

Introduction

Accented characters

Quantifiers

Equivalences

Inclusions

Miscellaneous symbols





Introduction

Accented characters

Mathematicians frequently use an accent to create a new variable from an old one. This is usually done to denote a mathematical object with some specific functional relationship with the old one.

All of the accents except arrow and slash (as far as I know) have more than one meaning. In the list below, I mention some common meanings, but mathematicians may and do define other meanings for the symbols.

Arrow

Bar

Check

Dot

Hat

Prime

Slash

A slash across a relational symbol means the resulting statement is false. For example, "$x\ne y$" means that the statement "$x = y$" is false; in other words, $x$ is not equal to $y$.

Star

The asterisk "*" may be used independently or as a modifier of a variable. In either case (except when it denotes multiplication) it is pronounced "star".

Star as modifier

Used independently

Tilde

Quantifiers

Quantifier symbols are used in logic.

Usage

Pronunciation

Pronouncing expressions using the two quantifiers involves a difference in English syntax.

Equivalences

The symbols $=,\,\,:=\,\,\equiv ,\,\,\sim ,\,\,\approx$ and $\cong$, along with many less common symbols, all denote relations concerned with approximate or exact equivalence.


$\boldsymbol{=}$

$\boldsymbol{:=}$

$\boldsymbol{\equiv}$

$\boldsymbol{\sim}$

$\boldsymbol{\approx}$

$\boldsymbol{\cong}$

Inclusions

The symbols $\subset \,,\supset \,,\subseteq \,,\supseteq \,,\varsubsetneq \text{, and}\varsupsetneq $, along with some less common symbols, all denote relations concerned with inclusion.

$\boldsymbol{\subseteq}$

"$A\subseteq B$" specifically includes the possibility that $A = B$. Note that that is the standard meaning of "subset": "$A$ is a subset of $B$" always allows $A=B$ and always allows $A$ to be the empty set.

$\boldsymbol{\subset}$

$\boldsymbol{\supset}$

$\boldsymbol{\supseteq}$

$\boldsymbol{\varsubsetneq}$

Miscellaneous symbols

$\boldsymbol{\times}$

$\boldsymbol{\in}$

$\boldsymbol{\varnothing}$


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