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Math Help - Continuity of sums, products, and quotients of functions

  1. #1
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    Continuity of sums, products, and quotients of functions



    I think this is probably pretty simple. Is this how its done?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by davismj View Post


    I think this is probably pretty simple. Is this how its done?
    Who says that f is continuous at a point means that \lim_{x\to x_0}f(x)=f(x_0). What about f:\{1\}\mapsto\{1\}?
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    there exits sequence (x_n) that converges to z_0. f and g are continuous at z_0 so f(x_n)\rightarrow f(z_0) and g(x_n)\rightarrow g(z_0) when n\rightarrow \infty. so \lim_{n\to \infty}(f+g)(x_n)=\lim_{n\to\infty}[f(x_n)+g(x_n)]=f(z_0)+g(z_0)=(f+g)(z_0) same with fg..
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