TeXipedia

vcentcolon

Creates a vertically centered colon symbol primarily used in mathematical notation for defining relations and functions.

Overview

Provides a more aesthetically pleasing alternative to the standard colon when defining mathematical relations, particularly in formal mathematical writing and typesetting.

  • Commonly used in combination with equals sign to create definition symbols (:=)
  • Preferred in professional mathematical typography over the regular colon for vertical alignment
  • Essential for maintaining consistent baseline alignment in mathematical expressions
  • Particularly valuable in contexts involving function definitions, set builder notation, and formal mathematical definitions

Examples

Defining a mathematical relation using centered colon equals.

f(x):=x2+2x+1f(x) \mathrel{\vcentcolon =} x^2 + 2x + 1 
f(x) \mathrel{\vcentcolon =} x^2 + 2x + 1

Defining a sequence using centered colon equals notation.

an:=1n2a_n \mathrel{\vcentcolon =} \frac{1}{n^2} 
a_n \mathrel{\vcentcolon =} \frac{1}{n^2}

Specifying a set definition with centered colon equals.

S:={x∈R:x>0}S \mathrel{\vcentcolon =} \{x \in \mathbb{R} : x > 0\} 
S \mathrel{\vcentcolon =} \{x \in \mathbb{R} : x > 0\}