HSC · Mathematics Extension 2 · Proof · also HSC Vectors · VCE Logic, Proof & Combinatorics live from the app

Proving Inequalities

Proving A is bigger than B without knowing either exactly: rearrange to a square, lean on the triangle inequality, deploy Cauchy-Schwarz or send in calculus. Inequality proofs are technique plus nerve. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.

mathematics extension 2 · proof · proving inequalitiesdrag it · it is yours
in the wild

Proving inequalities works like stacking evidence.

Proof isn't calculation — it's argument, where every line has to be forced by the one before it. Whether you're climbing an induction ladder or squeezing an inequality between what you know, you're never showing that something's true; you're showing it can't be false. The claim is the destination, but the reasoning is the whole mark.

Loose true facts sit in a pile — nothing proven yet, just raw material.

You lay each step on the last, every layer justified by the one below.

The stack reaches the top — the inequality now stands fully supported.

what examiners catch — Examiners test whether students can justify each step with valid reasoning and direction of inequality; the common trap is multiplying or dividing by negative expressions without reversing the inequality sign.
what you leave with

five things, not forty.

what's underneath

nothing here is a standalone fact.

knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 0 built on top. Each one says why, in a sentence, not as an arrow on a diagram.

this conceptproving inequalitiesProving inequalities involves showing one expression exceeds another through algebraic manipulation (completing the square to show non-negativity), applying standard inequalities like AM-GM or Cauchy-Schwarz, or using calculus to establish bounds without computing exact values.
sits under itlogical connectives and quantifiersbecause an inequality proof is a statement to be established, so the language of implication comes first
the rest of proof

3 more, same treatment.

Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.

proof by contradiction and counterexamplein the apprecursive formulas and notationin the applogical connectives and quantifiersin the app
this is one of 865

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knowherehsc mathematics extension 2proving inequalities