Re: X/0 DEFINED

From: Owen (oorionus_at_yahoo.com)
Date: 10/14/04 

Date: Thu, 14 Oct 2004 05:37:37 -0400

  "raydpratt" <raydpratt@hotmail.com> wrote in message
news:17b9a07c.0410140112.119f2a79@posting.google.com...
> Okay, you torque brains -- I need your help destroying my argument and
> convincing me in clear, simple English that I am wrong.
>
> I believe, to the depths of my thoughts, that X/0 can and should be
> defined.

  1/0 is defined but, it does not exist.

  1/x =df (the y: x*y = 1)

  1/0 = (the y: 0*y = 1), but, 0*y = 0 for all y, is a theorem.
  1/0 = (the y: 0 = 1)
  (0 = 1) is a contradiction
  1/0 = (the y: contradiction)
  (the y:contradiction) does not exist!
  therefore, 1/0 does not exist.

>
> X/0 = Infinity (Where X Does Not Equal 0)
>
> X/0 asks us, as with any division problem, to count the number of
> times that we may subtract the denominator from the numerator to the
> limit of the numerator, including any fractional part of the
> denominator that we can subtract from the numerator, and to give that
> count and any said fractional part as our answer. Clearly, we may
> subtract 0 from any non-zero amount an infinite number of times and
> will never reach the limit of any non-zero amount, so the answer is
> Infinity.
>
> The usual argument against this is that if X/0 = Infinity, then the
> inverse operation gives 0 x Infinity = X, which cannot be if the
> multiplicative identity principle of zero is to remain true that 0 x
> anything = 0.
>
> If, as a thought experiment, I assert that 0 x Infinity = X and that 0
> x Infinity = 0 is also true, then logically I must be asserting that
> Infinity has a comlex meaning, with at least two separate underlying
> premises leading to two different, true conclusions.
>
> Inductively, I can find agreement with my hypothesis by noting that
> Infinity as a quantity has no bound that can be fully touched by the
> power of multiplication by zero, thus allowing some X other than zero
> as a product, and at the same time note that Infinity distributively
> includes every possible finite number that can be touched by the
> multiplicative power of zero, thus leading to a total of zero.
>
> Not being satisfied with the mathematical logic of the particular X =
> 0 x Infinity, I nonetheless note that functionally, in relation to
> Infinity, there is no positional difference between 0 and X within
> infinity, for either one can be said to be the zero-point center of
> Infinity, depending only on where one chooses to start counting, both
> forward and backward. Thus, we have two distinct quantities, X and 0,
> that are nonetheless positionally equal on the number line in respect
> to the zero-point center of Infinity.
>
> Thus, my guts tell me that the nature of Infinity allows these math
> statements to be true, even though they seemingly violate fundamental
> principles of logic that state that something cannot be both what it
> is and what it is not. Properly viewed, logic is not violated here
> because we are merely saying the same thing in different ways.
>
> Taking the matter further, 0/0 = 1 because the division symbol tells
> us to count the number of times that we can subtract zero from zero to
> the limit of zero, but we reach the limit of zero the very first time
> that we perform the required process, and thus our answer is 1, a
> process 1.
>
> Likewise, 0/Infinity = X/Infinity (Where X Does Not = 0 or Infinity).
>
> The quotient in either case is zero because Infinity is so vast that
> no infinitesimal fraction of it can ever subtracted from zero or any
> finite number. More specifically, not even the smallest infinitesimal
> part of Infinity can be stated as one or more of the numerable parts
> of Infinity, for Infinity by definition does not have numerable parts,
> and thus no finite fraction of Infinity can ever be conceived of or
> subtracted from a finite number.
>
> Thus, the algebraic transformations of:
> 0/Infinity = X/Infinity (Where X Does Not = 0 or Infinity);
> 0 = X/Infinity (1/Infinity);
> 0 = X
> Are perfectly valid in respect to Infinity even though the equation is
> false as to the finite values of 0 and X. This seemingly violates the
> logical principle that something cannot be both true and false, but we
> may actually be looking at something with either one eye or the other
> closed at any given time, giving two different views of the same
> whole, but with a limited perspective in either case.
>
> It may not be without Supreme Reason that the Holy Bible warns us of
> the dangers of vain philosophy.
>
> Very Respectfully,
> Ray

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