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Real Analysis
2 notes · Last updated May 23, 2026
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ANALYSIS
Cauchy Criterion for Convergence
A sequence of real numbers converges if and only if it is a Cauchy sequence — providing convergence without knowing the limit.
\forall\varepsilon>0\;\exists N\in\mathbb{N}\;\forall m,n>N:\;|a_n-a_m|<\varepsilon
2026-05-18 Theorem
ANALYSIS
Heine-Cantor Theorem
A continuous function on a compact metric space is uniformly continuous.
\forall\varepsilon>0\;\exists\delta>0\;\forall x,y\in K:\;d(x,y)<\delta\Rightarrow d(f(x),f(y))<\varepsilon
2026-05-12 Theorem
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