Symmetry Breaking & WLOG

Order the variables before you start.

If a statement is symmetric, you may assume $a \ge b \ge c$ without loss of generality. That one line often halves the casework and unlocks rearrangement and Chebyshev, both of which need a known ordering.

The discipline: state the assumption explicitly and check the problem really is symmetric (or that you have handled the other orderings). A false WLOG is one of the most common ways a correct-looking solution loses marks.

For cyclic-but-not-symmetric expressions you may only rotate, not reorder, a distinction graders watch for.

Where it appears on Lemma: Level 5 onward, in nearly every inequality and combinatorics proof.

Train it on Lemma

Symmetry Breaking & WLOG unlocks at Level 5 of Lemma's eight-level ladder, with lessons that teach it and drills that make it stick. 125 lessons, 1206 curated problems and unlimited generated practice at six difficulties. Free to start, no card, and every paid plan opens with 3 free days.

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