1. Joined
    11 Nov '05
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    43938
    16 Apr '08 12:27
    In a book about number and infinity I found this question:
    "Can you prove, without circularity, that seven is a finite number?"

    Of course 7 is a finit number, it is just - 7, what else? And I know for sure that it is not infinite, then it must be finite, doesn't it?

    But strictly, if anyone claims that 7 is in fact finite, than he must be able prove it, or he just have to asume it.

    After a day or two (or if you want to discuss it further than that) I'll present the book's answer.
  2. Joined
    07 Sep '05
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    35068
    16 Apr '08 12:36
    Originally posted by FabianFnas
    In a book about number and infinity I found this question:
    "Can you prove, without circularity, that seven is a finite number?"

    Of course 7 is a finit number, it is just - 7, what else? And I know for sure that it is not infinite, then it must be finite, doesn't it?

    But strictly, if anyone claims that 7 is in fact finite, than he must be able prove ...[text shortened]... day or two (or if you want to discuss it further than that) I'll present the book's answer.
    I think the first thing I'd ask is "how are you defining a finite number?".
  3. Joined
    26 Nov '07
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    1085
    16 Apr '08 12:36
    Originally posted by FabianFnas
    In a book about number and infinity I found this question:
    "Can you prove, without circularity, that seven is a finite number?"

    Of course 7 is a finit number, it is just - 7, what else? And I know for sure that it is not infinite, then it must be finite, doesn't it?

    But strictly, if anyone claims that 7 is in fact finite, than he must be able prove ...[text shortened]... day or two (or if you want to discuss it further than that) I'll present the book's answer.
    Can you define a "finite number"? Are you meaning, essentially, a "finite cardinality" - where a "cardinal" is a number used to denote the size of a set (of objects/numbers/whatever)?
  4. Joined
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    1085
    16 Apr '08 12:371 edit
    Originally posted by mtthw
    I think the first thing I'd ask is "how are you defining a finite number?".
    oooh-you're fast!
  5. Pale Blue Dot
    Joined
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    21637
    16 Apr '08 12:38
    Originally posted by Swlabr
    oooh-your fast!
    Fastard!?
  6. Joined
    26 Nov '07
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    1085
    16 Apr '08 12:52
    Originally posted by Green Paladin
    Fastard!?
    not your fast - his fast.
  7. Pale Blue Dot
    Joined
    22 Jul '07
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    16 Apr '08 13:44
    Originally posted by Swlabr
    not your fast - his fast.
    Just being facetious.
  8. Subscribersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
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    52724
    16 Apr '08 13:51
    Originally posted by Green Paladin
    Just being facetious.
    or fast tidious.
  9. Joined
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    17881
    16 Apr '08 14:11
    Originally posted by sonhouse
    or fast tidious.
    fast-en your seatbelts
  10. Joined
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    43938
    16 Apr '08 14:16
    We are somewhat off-topic now, are we not...?
  11. Joined
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    16 Apr '08 16:16
    Define numbers.
  12. Standard membereldragonfly
    leperchaun messiah
    thru a glass onion
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    16 Apr '08 17:22
    What matthw said.
  13. Joined
    06 Apr '08
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    16 Apr '08 18:302 edits
    how about this:

    A set S is inifite if there exists a proper subset S' whose elements can be put into 1-to-1 corresponence with S ( there is a bijection from S' to S ).

    Hence a set S is finite if no proper subset S' can be put into 1-to-1 correspondence with S. Then the cardinality of S is an finite integer.

    Finally a number n is finite if there exists a finite set S whose cardinality c is such that Abs(n) < Abs(c)
  14. Joined
    31 May '07
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    696
    16 Apr '08 19:23
    Suppose 7 is infinite, then the title of this thread would contain an infinite number, but redhotpawn.com does not allow titles that are infinitely long. Thus, 7 is finite.

    Proof by contradiction.
  15. Sigulda, Latvia
    Joined
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    4048
    16 Apr '08 19:252 edits
    Originally posted by doodinthemood
    Suppose 7 is infinite, then the title of this thread would contain an infinite number, but redhotpawn.com does not allow titles that are infinitely long. Thus, 7 is finite.

    Proof by contradiction.
    If 7 is an infinite number, than no one could read this thread in his lifetime - Thread 91427. Hence, 7 is finite.

    Also proof by contradiction.
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