Recent content by BelaTalbot

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    Does Convergence of d(x_n, x) to 0 Imply x_n Approaches x?

    Homework Statement show that x_n converges to x if and only d(x_n, x) converges to 0. Homework Equations |x_n - x| < ε for all ε>0 The Attempt at a Solution well d(x_n,x) converges to 0 if d(x_n,x)<ε i just don't know how to relate that back to |x_n - x|
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    Undergrad Is a Bounded Set Always Finite or Can It Go to Infinity?

    So I guess what I'm really wondering is can a set be unbounded if it doesn't go to infinity? That's what I can't seem to wrap my brain around, because I feel that if a set doesn't go to infinity, there will always be a real number K larger than the members of the set.
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    Undergrad Is a Bounded Set Always Finite or Can It Go to Infinity?

    Is a bounded set synonymous to a set that goes to infinity? I feel like unless a set is (-infinity, n) or [n, infinity) it is not going to be unbounded. The other thing that I was wondering is can a set be neither open nor closed AND unbounded? Doesn't the definition of open/closed imply...