TeXipedia

equiv

Denotes mathematical equivalence or congruence between expressions, indicating a stronger relationship than simple equality.

Overview

Essential in mathematical proofs, logic, and formal reasoning where precise relationships between expressions need to be established.

  • Commonly used in number theory to show congruence modulo n
  • Appears frequently in abstract algebra to demonstrate equivalence relations
  • Used in formal logic to indicate logical equivalence between statements
  • Helpful in computer science for showing identical definitions or type equivalence

Examples

Defining a mathematical equivalence relation between two expressions.

x≡y(modn)x \equiv y \pmod{n} 
x \equiv y \pmod{n}

Showing logical equivalence between two boolean expressions.

p∧q≡¬(¬p∨¬q)p \land q \equiv \neg(\neg p \lor \neg q) 
p \land q \equiv \neg(\neg p \lor \neg q)

Defining a function in terms of another expression.

f(x)≡x2+2x+1f(x) \equiv x^2 + 2x + 1 
f(x) \equiv x^2 + 2x + 1