Composition of Continuous Functions is Continuous | Real Analysis
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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Real Analysis Course: • Real Analysis
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