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  1. M

    A Box Principle Problem

    it was....thanks!
  2. M

    A Box Principle Problem

    how do we get the inequality 1<= a1 <=.......<=a77 <= 132 ?? it hasn't been mentioned anywhere that the number of games played keeps increasing with each passing day, has it??
  3. M

    Math Q&A Game

    here's a proof of the question i had posted....thanks to matt grime(he sent me the proof) and i guess chingkui's done the same thing...so he gets to ask the next question... Let b be the square root of two, and suppose that the numbers If nb mod(1) are dense in the interval [0,1), then m+nb...
  4. M

    Prove that the sequence converges and find its limit

    By mere observation, it's quite clear that a_1 < a_2 <.......<a_n..... so, it's an increasing sequence... but i can't think of how we can show it's bounded...i mean,how do we use the recurrence relation?..and i guess, once we find the upper bound it would be easy to spot the limit of the...
  5. M

    Prove that the sequence converges and find its limit

    given a recurrence relation, a_1 =2^(1/2) and a_n = (2 +a_n-1)^1/2 ...prove that the sequence converges and find its limit.. are we supposed to begin by guessing the limit and the bounds ??
  6. M

    Probably quite simple but i'm stuck

    why not do something simpler? all you need to do is to find the point Q on the line where the normal vector passing through (3,-2,4) cuts it...that point looks like (1+t,4-3t,-2+2t) for some t. that is the t you need to find...and to do that use the fact that PQ is normal to the given...
  7. M

    Math Q&A Game

    i know it's a bad idea but looks like this is gonna be the end of this sticky... :grumpy: anyways...i want to work on the problem i posted....chingkui,could you elaborate the circle part...didn't quite get that...
  8. M

    Math Q&A Game

    Hi! Here is a problem I've been struggling with,so it appears real tough to me.just for the record...i haven't (yet) been able to write down a proof for it... prove that Z + 2^(1/2)Z is dense in R. (in words the given set is the set of integers + (square root of 2) times the set of...
  9. M

    Compact sets and homeomorphisms

    yeah...you're right... :redface:
  10. M

    Compact sets and homeomorphisms

    f being a homeomorphism...implies that f is invertible....
  11. M

    Math Q&A Game

    so...am i supposed post a new question,or not??
  12. M

    Math Q&A Game

    Ok…so I think I’ve got something (not a proof) here… Let A be a paired set containing an irrational point, say x. 0,x,1 belong to A and x-0 != 1-x, so there exists at least one additional point which is irrational or two points,at least one of which is irrational. In the first case, say , the...
  13. M

    Math Q&A Game

    i'm writing down the proof...i'm onto it ,head on... but there's something i'd like to clarify... in a paired set ,is it possible to have 3 pairs of elements having the same distance between them....or do we consider it to be exactly two pairs?
  14. M

    Math Q&A Game

    Let’s say you have an irrational x in A which is a paired set. You’re sure of 0,x and 1 being in the set. Now, obviously x-0 != 1-x .So there must be at least one additional point in the set (or two points p,q distinct from x such that p-q=x-0) .Now this point is irrational( in the other...
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