1. Joined
    28 Nov '05
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    24334
    13 Aug '06 15:511 edit
    Originally posted by XanthosNZ
    We're not talking 'knowing in a biblical sense'. That would make for an interesting party though.
    I was thinking more along the lines of
    I know him, he's Michael Jackson/Tony Blair/a.n. other celebrity
    but hey don't know me
  2. Stourbridge, England
    Joined
    14 Aug '06
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    2029
    14 Aug '06 17:52
    How about...

    A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check? (Note: 1 dollar = 100 cents.)

    Purely mathematical!
  3. Tempe, AZ
    Joined
    12 Oct '04
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    117487
    15 Aug '06 04:55
    Originally posted by Jamdog
    How about...

    A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check? (Note: 1 dollar = 100 cents.)

    Purely mathematical!
    Thx!
  4. Joined
    21 Jul '06
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    0
    15 Aug '06 05:017 edits
    Originally posted by chess kid1
    Thx!
    It ain't easy, kid. And why didn't you thank me for mine? :'( But just to prove that I'm not really upset, here's another one for your scrapbook:

    There is a subway line from the airport to the Hilbert hotel which operates as follows: there is a station at each ordinal number, and every station is assigned a unique ordinal. The subway stops at each station, in order. At each station people disembark and board, in order, as follows:

    i) if any passengers are on the subway, exactly 1 disembarks, then

    ii) aleph_0 passengers board the subway.

    Station 0 is at the airport, and the Hilbert hotel is at station w_1 (the first uncountable cardinal). The subway starts its journey empty. Aleph_0 passengers board the subway to the Hilbert hotel at the airport (station 0), and off it goes.

    When the subway pulls up to the Hilbert hotel at station w_1, how many passengers are on it? Is it 0, aleph_1, some determinate value in between, or indeterminate?
  5. Joined
    11 Jun '06
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    3516
    15 Aug '06 05:27
    Originally posted by ThudanBlunder
    It ain't easy, kid. And why didn't you thank me for mine? :'( But just to prove that I'm not really upset, here's another one for your scrapbook:

    There is a subway line from the airport to the Hilbert hotel which operates as follows: there is a station at each ordinal number, and every station is assigned a unique ordinal. The subway stops at ea ...[text shortened]... ssengers are on it? Is it 0, aleph_1, some determinate value in between, or indeterminate?
    your conditions don't make sense. there are aleph_1 stations but each has a unique cardinal number??
  6. Joined
    21 Jul '06
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    0
    16 Aug '06 14:47
    Originally posted by aginis
    your conditions don't make sense. there are aleph_1 stations but each has a unique cardinal number??
    That's not what I wrote.
  7. Joined
    20 Feb '06
    Moves
    8407
    17 Aug '06 08:39
    Originally posted by ThudanBlunder
    It ain't easy, kid. And why didn't you thank me for mine? :'( But just to prove that I'm not really upset, here's another one for your scrapbook:

    There is a subway line from the airport to the Hilbert hotel which operates as follows: there is a station at each ordinal number, and every station is assigned a unique ordinal. The subway stops at ea ...[text shortened]... ssengers are on it? Is it 0, aleph_1, some determinate value in between, or indeterminate?
    I'm not sure if this is correct/rigorous enough, as set theory isn't really my field, but as a few first tentative steps...

    The ordinals are arranged in increasing order, and we can think of them each as subsets of each of their successors, and supersets of all their predecessors. ie.

    1 subset of 2 subset of 3... subset of w...subset of w + 1...subset of w + 2...subset of w.2....subset of 3.w + 5... etc.

    So there are only countably many ordinals before the first uncountable ordinal.

    Since a countable number of countable sets is countable, I would say there is a countable number of people on the train.

    I would say this is determinate, unless there's some axiom of choice trickery going on that I've missed.
  8. Joined
    11 Jun '06
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    3516
    17 Aug '06 10:00
    Originally posted by ThudanBlunder

    there is a station at each ordinal number, and every station is assigned a unique ordinal.

    the Hilbert hotel is at station w_1 (the first uncountable cardinal).

    it is exactly what you wrote
  9. Joined
    21 Jul '06
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    0
    17 Aug '06 13:401 edit
    Originally posted by aginis
    it is exactly what you wrote
    Originally posted by aginis
    your conditions don't make sense. there are aleph_1 stations but each has a unique cardinal number??

    It? Do you mean the above? Hardly exact.
    'Ordinal' denotes position whereas 'cardinal number' denotes size.
    Bearing in mind that we are talking about transfinite ordinals, what exactly is your objection?
  10. Joined
    11 Jun '06
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    3516
    17 Aug '06 20:531 edit
    Originally posted by ThudanBlunder
    Originally posted by aginis
    [b]your conditions don't make sense. there are aleph_1 stations but each has a unique cardinal number??


    It? Do you mean the above? Hardly exact.
    'Ordinal' denotes position whereas 'cardinal number' denotes size.
    Bearing in mind that we are talking about transfinite ordinals, what exactly is your objection?[/b]
    sorry i mixed up the word cardinal and ordinal
    my problem is that you imply that there exists a one to one function from the set of stations (S) to the natural numbers. At the same time you are stating that the set S has cardinality aleph_1. thus a one to one function exists from a set of cardinality aleph_1 to a set of cardinality aleph_0. This is impossible.

    In other words if each station has a unique ordinal number attached to it then the set of stations must be countable (for example in order from least to greatest)
  11. Joined
    21 Jul '06
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    0
    20 Aug '06 02:51
    Originally posted by aginis
    sorry i mixed up the word cardinal and ordinal
    my problem is that you imply that there exists a one to one function from the set of stations (S) to the natural numbers. At the same time you are stating that the set S has cardinality aleph_1. thus a one to one function exists from a set of cardinality aleph_1 to a set of cardinality aleph_0. This is impossibl ...[text shortened]... d to it then the set of stations must be countable (for example in order from least to greatest)
    I thought that is what you meant.
    However, here we are not dealing with natural numbers but with transfinite numbers.

    http://mathworld.wolfram.com/TransfiniteNumber.html
  12. Joined
    15 Jun '06
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    16334
    27 Aug '06 02:021 edit
    Originally posted by XanthosNZ
    You attend a party along with N other people. Given any group of 4 party-goers you can be sure that at least one of the 4 knows the other three. Prove that at least one person knows all others at the party.

    EDIT: I have saved this thread.
  13. Standard memberIM4Y2NV
    Dadohalic
    Finger tip talking.
    Joined
    31 Jul '06
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    29649
    27 Aug '06 02:38
    Originally posted by tomtom232
    Originally posted by aginis
    assume that no guest knows all the other guests. then each guest does not know (at least) one other person. since in any group of 4 people you must know at least 1 there are a maximum of 2 strangers per guest. now according to our assumption if i pick a random guest A from the party there Exists guest B such that A,B are strangers. now we pick a third guest C if A,B,C are all strangers then they've reached their maximum of two strangers each so any fourth guest D must know them all (If there are only 4 guests then we are done) but again according to our assumption there Exists a fifth guest E who is a stranger to D. take the group A,B,D,E. A is a stranger to B who is a stranger to A and D is a stranger to E who is a stranger to D, this contradicts the assumption so at least one guest knows everyone.

    in fact this shows that if A,B,C are all strangers then all the other guests know everyone at the party.
  14. Sigulda, Latvia
    Joined
    30 Aug '06
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    4048
    03 Sep '06 19:30
    A purely mathematical riddle - 1.5 chickens lay 1.5 eggs in 1.5 days. How many eggs will 9 chickens lay in 9 days?
  15. Standard memberTheMaster37
    Kupikupopo!
    Out of my mind
    Joined
    25 Oct '02
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    20443
    03 Sep '06 22:48
    Originally posted by kbaumen
    A purely mathematical riddle - 1.5 chickens lay 1.5 eggs in 1.5 days. How many eggs will 9 chickens lay in 9 days?
    54
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