Recent content by philosophking

  1. P

    Why Are the Rationals Not Locally Compact?

    yeah, i shouldn't have said "compact subset of Q". I should have just said "any subset of Q". sorry for the confusion!
  2. P

    Why Are the Rationals Not Locally Compact?

    This is great, thank you so much for the help. It is indeed the subspace topology that I'm working with (I overlooked that very large detail). Also, wouldn't any compact subset of Q with the subspace topology contain an infinite number of points? Because between any two numbers there is an...
  3. P

    Why Are the Rationals Not Locally Compact?

    I'm having a hard time understanding why the rationals are not locally compact. The definition of local compactness is that every neighborhood of x in X is contained in some compact subset of X. But what are the compact subsets of X? I think this is my biggest problem. I know that the...
  4. P

    Have You Considered This Trick for Finding the Derivative of a Cubic Function?

    but i don't think i understand. how is dy/dx [ y^3 ] = 3y^2? isn't it zero?
  5. P

    What are some invariants that can be used to distinguish between two spaces?

    Great, thanks a lot you guys. That was a big help. I guess it just depends on being creative in your map-defining.
  6. P

    What are some invariants that can be used to distinguish between two spaces?

    How would you do that? I saw someone once parametrize to make it work, but I guess I just don't know how one would go about doing that.
  7. P

    What are some invariants that can be used to distinguish between two spaces?

    One question I've had lately in my independent study of topology is the problem of how to show two sets are homeomorphic to each other. I am not sure how I would go about doing this in a general, or even specific case. One problem that wants me to demonstrate this is in Mendelson: Prove that...
  8. P

    How many problems should you do when teaching yourself?

    Also, from my experience, doing the problems makes you really learn definitions. Oftern when I am self-studying topology, i use the problems as a way of testing myself on simple definitions by writing them in the actual problem, then going after them that way. They also help you integrate...
  9. P

    Programs Double Majors & GREs: Math & Physics Tests for Grad School

    I've heard there's an exception to this rule with mathematics and economics (if going to grad school for economics). Can anyone validate/disprove this?
  10. P

    Can anyone provide a proof for the Bolzano-Weierstrass Theorem claim?

    "I am also, by the way, moving this to "College Homework". If it isn't homework, or reviewing for a test, I can't imagine why you would be doing it!" I have a slight problem with this. I am currently doing an independent study in topology with Munkres and also Mendelson, and my main strategy...
  11. P

    Disproving Uniform Convergence of f_n(x) on [0,1]

    I'm sorry, I'm not sure what you mean by "limit function". Although I think I now know where Fourier was going. The definition of uniform convergence does not depend on x. That means I can take any two x in the domain and their images must necessarily converge to less than epsilon. But say...
  12. P

    Disproving Uniform Convergence of f_n(x) on [0,1]

    You get the sequence 1,1,1,1,... which converges? I guess I don't know where you're going with that.
  13. P

    Disproving Uniform Convergence of f_n(x) on [0,1]

    I haven't done uniform convergence since last year when I took analysis, and now I have this problem for topology (we're studying metric spaces right now) and I can't remember how to disprove uniform convergence: f_n: [0,1] -> R , f_n(x)=x^n Show the sequence f_n(x) converges for all x in...
  14. P

    Sample Space of Selecting 5 Balls Without Replacement

    If they were selected one at a time, what would the final sample space be for each possible combination? I'll give you a hint: I don't think what you did and what the answer to the problem is differs so much :)
  15. P

    What Are Complex Numbers and How Can They Simplify Your Calculations?

    "buy a ti 89 or voyage 200 and your problems are forever solved" if his problem is understanding how certain things work, then i think his problem would stay untouched if he bought one of these caluclators.
Back
Top