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Re: [PrimeNumbers] Digest Number 1127

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  • chasag@aol.com
    A nearly infinite number can be defined if one cares to. Orders of infinity have been defined, so why not suborders? [Non-text portions of this message have
    Message 1 of 3 , Nov 1, 2003
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      A nearly infinite number can be defined if one cares to. Orders of infinity
      have been defined, so why not suborders?


      [Non-text portions of this message have been removed]
    • Andy Swallow
      ... You speak of infinity like it is some sort of black hole, with an event horizon, beyond which all integers get sucked in to being infinite. This is not
      Message 2 of 3 , Nov 1, 2003
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        On Sat, Nov 01, 2003 at 06:13:52PM -0500, chasag@... wrote:
        > Ther must be very very large numbers just on the verge of infinity, After
        > that there must be a prime gap reaching to infinity. Thus there is a finite
        > number of primes. After all if one can imagine infinity, one can imagine
        > the verge of infinity.

        You speak of infinity like it is some sort of black hole, with an event
        horizon, beyond which all integers get 'sucked in' to being infinite.
        This is not true. Infinity is a convenient concept, used when discussing
        quantities which increase without bound. Euclid's tiny little proof
        shows that the number of primes has no bound, and is therefore not
        finite.

        Andy
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