TeXipedia

eqcolon

Represents a colon-based equality symbol used to define mathematical expressions or indicate definitions.

Overview

Primarily used in mathematical writing to denote definitions or to establish equivalence relationships between expressions. This symbol combines the visual elements of both an equals sign and a colon, making it particularly useful in:

  • Formal mathematical definitions where precise notation is required
  • Set theory and abstract algebra when defining new terms
  • Logic and proof writing where explicit definitions need to be distinguished from standard equality
  • Academic papers and textbooks where mathematical concepts are being introduced

Examples

Defining a mathematical sequence explicitly.

xn∹1n2for n≥1x_n \eqcolon \frac{1}{n^2} \quad \text{for } n \geq 1 
x_n \eqcolon \frac{1}{n^2} \quad \text{for } n \geq 1

Introducing a new mathematical function definition.

f(x)∹x2+2x+1f(x) \eqcolon x^2 + 2x + 1 
f(x) \eqcolon x^2 + 2x + 1

Defining a set using explicit conditions.

S∹{x∈R:x>0}S \eqcolon \{x \in \mathbb{R} : x > 0\} 
S \eqcolon \{x \in \mathbb{R} : x > 0\}