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  • :coffee:

    Best Answer - Chosen by Asker
    Two problems with this question.

    1. Circle with infinite circumference is impossible.

    2. You can't do normal arithmetic with "infinity".
    So, if (inf) = pi D, we cannot conclude that
    That therefore pi = 1 since D = (inf) as well.

    It would be JUST as valid (or invalid) to conclude
    pi = 1/2, since if the diameter is infinite, so is the radius.
    and C = 2 pi r. (inf) = 2 pi (inf), "pi = 1/2". (NOT)

    Here is a case in point:
    The definition of equality in counting is:
    if two sets can be put in 1-1 correspondence
    then they have an equal number of elements.

    Consider the integers: 1, 2, 3, 4, 5, ......
    There are an infinite number of them, because,
    like the Energizer Bunny, they just keep going.

    Now consider the even integers: 2, 4, 6, 8, 10, .....

    One "obvious" conclusion is that there are only half as
    many because the even integers are a subset of
    the integers, and well ... what about all the odd integers ?

    There are just as many of them, because we can make
    a 1-1 correspondence:
    1 3 5 7 9 ....
    2 4 6 8 10 .....
    Even(i) = Odd(i) + 1

    So (#Evens) + (#Odds) = (#Integers)
    (#Evens) * 2 = (#Integers)
    (#Evens) = (#Integers) / 2

    But .... not so fast ...
    We can also make this 1-1 correspondence:

    1 2 3 4 5 .....
    2 4 6 8 10
    Even(i) = 2 * Integer(i)

    So we conclude that there are JUST AS MANY Evens as Integers (never mind the Odds !)

    So for this (Inf) we have 2 * (Inf) = (Inf) !!
    (And that does not prove 2=1, either)

    (Now it turns out the Real numbers, or just the irrational
    numbers CANNOT be put in 1-1 correspondence with
    the integers, but that's another story.)

    Even with the "lowest" infinity, called Aleph-0, the normal rules of arithmetic do not apply.


    I must confess that I have no clue what the fuck they are talking about because I found this on google :D
    Yes, inclined to agree. I don't know if it's old age creeping up on me or just that the topics have all been pretty much exhausted, but a lot of the talk seems to be getting tired.
    I still haven't gotten used to this feature with the visitor messages. I always miss them. OK....

    Pop, looks like I missed Jemfest, but you already knew that. LOL. Next time!

    Eric, nothing much. Another day, another dollar....or for us low-life engineers, it's another penny.

    Davy, I haven't been on Jemsite that much because it kinda became boring to me. I'm not really finding any conversation that sparks my interest to join. I usually go there once every one or two days just to see what's going on, but I'm only there for a few minutes. Same thing with here. I just haven't found a conversation that I care to get into. But I've been on both sites more recently than in the recent past.
    Hiya Courtney. Haven't seen much of you on Jemsite recently ...... you fighting with someone?
    I had no idea I had all these messages here. *slaps forehead* Sorry you all. Going to try and make it to Jemfest.
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