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Mathematics vocabulary · Proofs and Mathematical Writing

Without loss of generality

Meaning in mathematics, with examples

phraseAdvanced term

In mathematics, without loss of generality means: A phrase in proofs meaning that only one case is treated because the other cases work in exactly the same way, as in 'assume a ≤ b'.

In Turkish: genelliği bozmadan, genellikten bir şey kaybetmeden

How it is used

Usually shortened to WLOG in lecture notes but read aloud in full. A typical sentence is 'Without loss of generality, assume x ≥ y'. It should only be used when the cases really are symmetric.

Example sentences

  1. Without loss of generality, let a be the largest of the three numbers.

  2. You can't say 'without loss of generality' here, because the two cases aren't symmetric.

Common collocations

  • without loss of generality, assume
  • WLOG
  • by symmetry
  • without loss of generality, let
  • let x beA fixed phrase used to introduce a variable or an assumption at the start of a solution or proof, as in 'Let x be the number of tickets sold'.
  • proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.
  • it follows thatA linking phrase used in proofs and solutions to show that the next statement is a logical result of what has just been shown.
  • lemmaA smaller statement, proved on its own, that is used as a step towards proving a larger theorem.

More terms: Proofs and Mathematical Writing

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