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What is infinity?

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  • Kent Nguyen
    Infinity has never clearly explained to me while I was in school. Maybe you guys can help me. The following are a list of True or False question. True or
    Message 1 of 5 , Nov 30, 2001
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      Infinity has never clearly explained to me while I was in school. Maybe you
      guys can help me. The following are a list of True or False question.

      True or False:
      1) Infinity is a number.
      2) Infinity is an odd number.
      3) Infinity is a prime number.

      Thanks,
      --kent
    • Jud McCranie
      ... Yes, but it isn t an integer or real number. http://mathworld.wolfram.com/Infinity.html ... False. ... False.
      Message 2 of 5 , Nov 30, 2001
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        At 07:49 PM 11/30/2001 +0000, Kent Nguyen wrote:
        >Infinity has never clearly explained to me while I was in school. Maybe you
        >guys can help me. The following are a list of True or False question.
        >
        >True or False:
        >1) Infinity is a number.

        Yes, but it isn't an integer or real number.

        http://mathworld.wolfram.com/Infinity.html

        >2) Infinity is an odd number.

        False.

        >3) Infinity is a prime number.

        False.


        +---------------------------------------------------------+
        | Jud McCranie |
        | |
        | Programming Achieved with Structure, Clarity, And Logic |
        +---------------------------------------------------------+
      • Chris Caldwell
        ... Depends on your definition of numbers (my favorite is in Conways on numbers and games ). Infinity is not an integer. It is a member of a set of numbers
        Message 3 of 5 , Nov 30, 2001
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          At 07:49 PM 11/30/01 +0000, Kent Nguyen wrote:
          >Infinity has never clearly explained to me while I was in school. Maybe you
          >guys can help me. The following are a list of True or False question.
          >
          >True or False:
          >1) Infinity is a number.

          Depends on your definition of numbers (my favorite is in Conways "on
          numbers and games").
          Infinity is not an integer. It is a member of a set of numbers called the
          "extended reals (+infinity,
          and -infinity)". It is many numbers if you are speaking of the cardinal
          numbers (sizes of sets).

          >2) Infinity is an odd number.

          No, it is not an integer.

          >3) Infinity is a prime number.

          No, it is not an integer.
        • jack@brennen.net
          ... Both of the statements Chris made are true by definition. However, this leads to an interesting question. What is the proper way to say (for instance):
          Message 4 of 5 , Nov 30, 2001
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            --- In primenumbers@y..., Chris Caldwell <caldwell@u...> wrote:
            > >2) Infinity is an odd number.
            >
            > No, it is not an integer.
            >
            > >3) Infinity is a prime number.
            >
            > No, it is not an integer.

            Both of the statements Chris made are true by definition.

            However, this leads to an interesting question.

            What is the "proper" way to say (for instance):

            1. Compute the sum of 1/p^2 as p ranges over the prime numbers
            from 2 to infinity.

            or

            2. Compute the product of 1+(1/x^2) as x ranges over the
            odd numbers from 1 to infinity.


            I think these are both proper and it is understood that the
            "infinity" reference is not to an actual number but is rather
            a succinct way of stating that the range goes on without bound.

            However, I could understand how someone reading (1) or (2) above
            might think that infinity is a prime number or an odd number...
          • Phil Carmody
            ... as p ranges over the unbounded set of prime numbers greater than or equal to 2. ? Which certainly could be shortened without any wild ambiguity. ...
            Message 5 of 5 , Nov 30, 2001
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              On Fri, 30 November 2001, jack@... wrote:
              > --- In primenumbers@y..., Chris Caldwell <caldwell@u...> wrote:
              > > >2) Infinity is an odd number.
              > >
              > > No, it is not an integer.
              > >
              > > >3) Infinity is a prime number.
              > >
              > > No, it is not an integer.
              >
              > Both of the statements Chris made are true by definition.
              >
              > However, this leads to an interesting question.
              >
              > What is the "proper" way to say (for instance):
              >
              > 1. Compute the sum of 1/p^2 as p ranges over the prime numbers
              > from 2 to infinity.

              as p ranges over the unbounded set of prime numbers greater than or equal to 2.
              ?

              Which certainly could be shortened without any wild ambiguity.

              > or
              >
              > 2. Compute the product of 1+(1/x^2) as x ranges over the
              > odd numbers from 1 to infinity.

              ... unbounded set of odd numbers greater than or equal to 1.

              > I think these are both proper and it is understood that the
              > "infinity" reference is not to an actual number but is rather
              > a succinct way of stating that the range goes on without bound.

              Infinity as a bound => no finite bound => no bound

              > However, I could understand how someone reading (1) or (2) above
              > might think that infinity is a prime number or an odd number...

              You don't explicitly say whether the set is open or closed. Why should someone assume a closed set, and thus an included upper bound, rather than a half-open set, with an excluded upper bound? The danger is more that of people infering something erroneous from something not said, rather than misinterpreting something actually said. Errors like that are always harder to prevent. You can't exclude every possible inference, I'm sure.

              <JSH> What ring were you working in, again? </JSH>

              Phil

              Don't be fooled, CRC Press are _not_ the good guys.
              They've taken Wolfram's money - _don't_ give them yours.
              http://mathworld.wolfram.com/erics_commentary.html


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