What is the difference between differentiable and continuous $\begingroup$ @user135626: What I wrote is correct You are misreading it I'm not saying the derivative is zero, I'm saying that if the derivative exists, the numerator of the difference quotient necessarily converges to zero (not that the difference quotient itself must)
continuity - What is a continuous stochastic process? - Mathematics . . . Isn't this violating the definition of continuous stochastic process or is it that I have to keep $\omega$ constant throught out the process ? Also, is $\omega$ in the definition of continuous stochastic process the outcome at any point of time or is it the string of the outcomes that occurs till time infinity?
is bounded linear operator necessarily continuous? Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider context of topological vector spaces, while the proposition mentioned here fails: there are bounded discontinuous linear operators, yet every continuous operator remains
Difference between continuity and uniform continuity I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions For example, my book
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