Pure · Proof
Chapter 1 · 3
The idea
Proof by deduction
Direct proof — starting from things known to be true and reasoning in valid algebraic steps to the conclusion. Representing the general case (2n, 2n+1, consecutive integers), "show that" manipulations, completing the square for positivity, and always finishing with a clear conclusion.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
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Pure · Proof
Proof by deduction
Direct proof — starting from things known to be true and reasoning in valid algebraic steps to the conclusion. Representing the general case (2n, 2n+1, consecutive integers), "show that" manipulations, completing the square for positivity, and always finishing with a clear conclusion.
Why it works
From known truths to the claim
"Prove that the sum of the squares of two consecutive integers is odd." You could check , and — both odd — and prove precisely nothing. A proof by deduction (a direct proof) starts from statements already known to be true — definitions and established results — and moves by valid steps to the thing you must show. Done properly it settles the claim for every case at once, which is exactly why checking a few examples is not a proof.Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
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