Re: VOTE on whether 1/oo = 0

From: |-|erc (gotch_at_beauty.com)
Date: 07/14/04

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    Date: Wed, 14 Jul 2004 00:28:30 GMT

    > Does 1/oo = 0 ?
    >

    Thanks to all participants and Kent for his insightful rebuttal on voting and maths.

    No is what I thought that is why I was surprised when Barb Knox claimed yes.

    With all the other bizzare interpretations of maths I was taught that people
    around here take as correct I had to check.

    > >> >Or does 1/oo = 0 now?
    > >>
    > >> It certainly does. For example, have a look at
    > >> <http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html>, item (7).
    > >> Didn't you already know that?
    > >
    > >"these improper elements are not real numbers, and that this system of
    > >extended real numbers is not a field."
    > >
    >
    > Apparently your super-powers do not include reading comprehension. From the
    > same web page:
    > 'The above statements which define results of arithmetic operations on oo may
    > be considered as abbreviations of statements about determinate limit forms.
    > For example, -(+oo) = -oo may be considered as an abbreviation for "If x
    > increases without bound, then -x decreases without bound."'

    Which means
    1/oo = 0 is an abbreviation for lim(x->oo) 1/x = 0

    That first "=" is not equals. You are better off using notation
    1/oo <=> 0

    **

    I do have a liberal perspective on the topic also.

    IF you define division by infinity to start with
    THEN you could assign that result as 0.
    IF mice flew to the moon they would eat green cheese. That also could be correct!

    But like someone pointed out a/b = c <-> a/c = b which doesn't work with division by 0.
    So even you have formula where 1/oo is parsed the result is likely to be undefined still.

    Herc

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