TeXipedia

equalscolon

Represents a combination of equals and colon symbols, commonly used in mathematical definitions and formal proofs.

Overview

Serves as a specialized relational operator in mathematical writing, particularly when defining new terms or establishing formal relationships between expressions.

  • Often appears in formal mathematical texts and proofs where precise notation is essential.
  • Used to indicate that the left-hand side is being defined as equal to the right-hand side.
  • Provides a more formal alternative to the simple equals sign when making definitions.
  • Common in abstract algebra, set theory, and theoretical mathematics where rigorous definitions are crucial.

Examples

Defining a function using equals-colon notation.

f(x)≕x2+2x+1f(x) \equalscolon x^2 + 2x + 1 
f(x) \equalscolon x^2 + 2x + 1

Specifying a set definition with equals-colon.

S≕{x∈R:x>0}S \equalscolon \{x \in \mathbb{R} : x > 0\} 
S \equalscolon \{x \in \mathbb{R} : x > 0\}

Declaring a variable assignment in mathematical notation.

n≕2k where k∈Nn \equalscolon 2^k \text{ where } k \in \mathbb{N} 
n \equalscolon 2^k \text{ where } k \in \mathbb{N}