Proofs

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

Showing 3 proofs in Real Analysis.

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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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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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Proof that every convergent sequence is bounded

This theorem is a standard follow-up to the definition of convergence because it shows how one tail estimate plus finitely many early terms gives a global bound on the whole sequence.

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Proofs

Proof that the limit of a convergent sequence is unique

Epsilon-delta proof that limx→2​x2=4

Proof that every convergent sequence is bounded

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