Thursday, 3 October 2013

real analysis - Is f(n)=n, where ninmathbbZ with the Euclidean metric continuous on mathbbZ?

According to the definition of continuity, given any n0Z, ϵ>0, δ>0 such that nZ and dX(n,n0)<δdY(f(n),f(n0))<ϵ holds when δ=ϵ. So I conclude that this graphically discrete function is continuous... Is there anything wrong?

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real analysis - How to find limhrightarrow0fracsin(ha)h

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