Caught on tape by an undercover CIA agent were William Elliot's words:
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WE> Get the idea? Continue infinitely. limits of limits of limits, limits
WE> of limits of limits of limits, limits of... ***. (*** means ...
WE> repeated ... times). Is your mind boggled by now? It should be
WE> otherwise it wouldn't be infinite, now would it? -)
Yeah, but the limit *is* infinity. Another way of describing
infinity with some mathematical operations is "undefined," as in
division by zero. Infinity *is* undefinable.
WE> But I'm describing infinity, and what I've described so far is just a
WE> beginning, else it wouldn't be infinity, now would it. -) How big can
WE> infinity get? Take an infinite number N and create larger infinities
WE> N^N, N^N^N, .... N times, and you've done next to nothing but express
WE> the expressible. -) Yet the mystics admonish infinity is
WE> inexplicable.
But really, all this is just word and math games, for even if one
infinite set is shown to be larger than another, say the set of all
integers vs the set of even integers, how can you really tell? Who has
seen the end of either series to know? I can logically see that the
latter should be half the size of the former, but my base instincts
argue against this, since neither set has an end? Again, how can you
really tell?
... I used spot remover on my dog. Now he's gone.
--- PPoint 2.05
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* Origin: Seven Wells On-Line * Nashville, TN (1:116/30.3)
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