TeXipedia

Eqcolon

Represents a colon-based equality symbol used to denote definitions or equivalences in mathematical writing.

Overview

Serves as a specialized mathematical punctuation mark that combines equality with a colon, primarily used in formal mathematical definitions and theoretical computer science.

  • Common in set theory and abstract algebra for introducing formal definitions
  • Provides a more precise alternative to standard colons or equality signs when defining new terms
  • Often appears in academic papers and textbooks where mathematical rigor is essential
  • Particularly useful in contexts where distinguishing between different types of equality relations is important

Examples

Defining a mathematical function using the colon equals notation.

f(x)−∷x2+2x+1f(x) \Eqcolon x^2 + 2x + 1 
f(x) \Eqcolon x^2 + 2x + 1

Introducing a sequence definition with explicit notation.

an−∷1n2for n≥1a_n \Eqcolon \frac{1}{n^2} \quad \text{for } n \geq 1 
a_n \Eqcolon \frac{1}{n^2} \quad \text{for } n \geq 1

Defining a set using explicit construction.

S−∷{x∈R:x>0}S \Eqcolon \{x \in \mathbb{R} : x > 0\} 
S \Eqcolon \{x \in \mathbb{R} : x > 0\}