Recent content by renjean

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    Uniform Continuity and Supremum

    Does x*sin(1/x) work since its derivative is undefined at x=0 which is in [-1,1]?
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    Uniform Continuity and Supremum

    thanks!
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    Cauchy sequences and continuity versus uniform continuity

    Homework Statement This isn't really a problem but it is just something I am curious about, I found a theorem stating that you have two metric spaces and f:X --> Y is uniform continuous and (xn) is a cauchy sequence in X then f(xn) is a cauchy sequence in Y. Homework Equations This...
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    Showing that Increasing sequences of natural numbers is uncountable

    That helps a lot! Thank you to the both of you.
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    Showing that Increasing sequences of natural numbers is uncountable

    Homework Statement Show that A, the set of all increasing sequences of natural numbers is uncountable Homework Equations I know that the natural numbers themselves are countable. The Attempt at a Solution I am thinking of using some sort of diagonal argument to prove this.
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    Limits of a function's derivative and how it relates to a function.

    ah! that helps a lot. thanks for the hint!
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    Limits of a function's derivative and how it relates to a function.

    Homework Statement Prove or disprove: if lim x->b (from the left) f'(x) = infinity then lim x->b (from the left) f(x) = infinity Homework Equations my gut instinct is that this is false. The Attempt at a Solution I have thought of many counterexamples but none of them seem to...