Composition of Continuous Functions is Continuous | Real Analysis

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We prove the composition of continuous functions is continuous using the sequence definition of continuity. We assume g is a function from A to B, and f is a function from B to the reals. We assume g is continuous at c in A and f is continuous at g(c) in B. We can then apply the sequential definition of continuity to prove that any sequence in A converging to c has a sequence of images converging to f(g(c)). #realanalysis

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WrathofMath
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Never miss a lecture from Wrath of Math! 😊

punditgi
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Please make a video of convergence pointwise

michaelquiroz
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It seems to me that the proof would be easier to follow if you elaborate some more lines with more notations. No ambiguity would be left

nonentity
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This is so helpful for a student stuck in the notation of real analysis❤

garysu