TeXipedia

because

Indicates a logical reason or justification in mathematical proofs and logical arguments.

Overview

Essential in formal mathematical writing and logical discourse where explicit reasoning needs to be shown. Commonly found in:

  • Mathematical proofs where each step's justification needs to be clear
  • Logical arguments and formal reasoning
  • Set theory and abstract algebra explanations
  • Computer science and discrete mathematics proofs

Often paired with 'therefore' (∴) in formal deductions, helping create clear chains of logical reasoning in academic and theoretical work.

Examples

Stating a mathematical proof reason using 'because'.

x=y∵x−y=0x = y \because x - y = 0 
x = y \because x - y = 0

Logical implication with explanation.

△ABC is isosceles∵AB=AC\triangle ABC \text{ is isosceles} \because AB = AC 
\triangle ABC \text{ is isosceles} \because AB = AC

Mathematical reasoning in set theory.

x∈A∩B∵x∈A and x∈Bx \in A \cap B \because x \in A \text{ and } x \in B 
x \in A \cap B \because x \in A \text{ and } x \in B