Recent content by oma12

  1. O

    Every infinite set has a countable dense subset?

    i think i get what u're saying.. so for every q rational for a fixed n we choose and x in the set that belongs to (q-1/n ; q+1/n). Giving us a set of countable x's, then we do this for all n, which is a countable number of countable sets, thus countable. But i am having a little trouble...
  2. O

    Every infinite set has a countable dense subset?

    well we know that the rationals are countable and dense in the reals. but umm..i donno, at this point i am lost about how to prove this.
  3. O

    Every infinite set has a countable dense subset?

    ok, since this is real analysis, i think i am mostly interested in the real line. so how do i go about solving it for the reals?
  4. O

    Limit of x^1/x as x Approaches Infinity: Simplified Using ln and e

    ok so it simplifies to e^((lnx)/x) and the limit of (lnx)/x is 0, so? e^0 = 1
  5. O

    Every infinite set has a countable dense subset?

    Homework Statement Prove that every infinite set has a countable dense subset. Homework Equations The Attempt at a Solution I have almost no idea how to solve this problem of my analysis homework. I was thinking that i need to show that there is a countable subset that has all...
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