Proofs

Browse a catalog of interesting and common proofs, from core analysis and linear algebra arguments to standard proof techniques worth knowing well.

ProofReal AnalysisProof Builder

Proof that the limit of a convergent sequence is unique

A convergent sequence cannot settle down to two different numbers. The proof is short, but it is a good model for how contradiction and the definition of limit work together.

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ProofLinear AlgebraProof Builder

Proof that the kernel of a linear map is a subspace

This is a standard linear algebra proof because it packages the subspace test into one reusable pattern: show zero is inside, then check closure under addition and scalar multiplication.

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ProofReal AnalysisProof Builder

Epsilon-delta proof that $lim_{x \to 2} x^{2} = 4$

This proof is common because it shows the standard move in early analysis: factor the expression, then bound the extra factor by forcing $x$ into a smaller interval first.

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Proofs

Proof that the limit of a convergent sequence is unique

Proof that the kernel of a linear map is a subspace

Epsilon-delta proof that limx→2​x2=4

Epsilon-delta proof that $lim_{x \to 2} x^{2} = 4$