Is (a^x)*(1/a^x)=1?

V.Gopal

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Oct 25, 2002, 12:32:48 PM10/25/02

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Is the product of a^x and 1/a^x equal to unit or 1 both in physics and
in mathematics? How do (a^x)*1/a^x, x*1/x and XY differ from one
another (if XY=1)?

Helmut Wabnig

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Oct 26, 2002, 3:19:49 AM10/26/02

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On 25 Oct 2002 09:32:48 -0700, vgop...@rediffmail.com (V.Gopal)
wrote:

>Is the product of a^x and 1/a^x equal to unit or 1 both in physics and
>in mathematics? How do (a^x)*1/a^x, x*1/x and XY differ from one
>another (if XY=1)?

look what will happen if x >> infinite.
we get: infin. divided by zero.

w.

John Christiansen

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Oct 26, 2002, 6:59:04 AM10/26/02

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I suggest you re read the original post Helmut Wabnig, what we really get is
x/x which is always 1.

John Christiansen

"Helmut Wabnig" <hwXa...@aXon.at> skrev i en meddelelse
news:3dgkrugfkpgbbanf2...@4ax.com...

David W. Cantrell

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Oct 26, 2002, 10:41:33 AM10/26/02

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"John Christiansen" <super...@mail1.stofanet.dk> wrote:
> I suggest you re read the original post Helmut Wabnig,
> what we really get is x/x which is always 1.

No, not always! If there is anything of interest here, it is the fact
that x/x is not always 1. Of course, if x is a _nonzero_ real or complex
number, then x/x is indeed 1. But if x = 0, then x/x is normally considered
to be undefined in mathematics. [FWIW, outside of mathematics, we find that
0/0 is NaN in standard floating-point arithmetic, 0 in J, and 1 in APL.]

David Cantrell

> "Helmut Wabnig" <hwXa...@aXon.at> skrev i en meddelelse
> news:3dgkrugfkpgbbanf2...@4ax.com...
> > On 25 Oct 2002 09:32:48 -0700, vgop...@rediffmail.com (V.Gopal)
> > wrote:
> >
> > >Is the product of a^x and 1/a^x equal to unit or 1 both in physics and
> > >in mathematics? How do (a^x)*1/a^x, x*1/x and XY differ from one
> > >another (if XY=1)?
> >
> > look what will happen if x >> infinite.
> > we get: infin. divided by zero.

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V.Gopal

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Oct 26, 2002, 3:29:48 PM10/26/02

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Helmut Wabnig <hwXa...@aXon.at> wrote in message news:<3dgkrugfkpgbbanf2...@4ax.com>...

I physics if a=1/2 and between every two consecutive terms the period
is constant (half life time) then a^x describes the process of natural
radioactive decay. If time is not included in a^x even the 'element'
we are talking about are different. a^x/a^x can in no case be equal to
1 and it is not hyperbola. XY=1 supposedly gives a hyoerbola because Y
between 0 and 1 has as many number of numbers as X between 1 and
infinity, and X between 0 and 1 has as many number of numbers as Y
between 1 and infinity. No body can prove that x*1/x is hyperbola.
x/x=1 and one increases continuously. 1 is not definable.

Darren G. Lorent

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Oct 26, 2002, 4:16:43 PM10/26/02

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"John Christiansen" <super...@mail1.stofanet.dk> wrote in message news:<3dba7576$0$1010$ba62...@nntp04.dk.telia.net>...

> I suggest you re read the original post Helmut Wabnig, what we really get is
> x/x which is always 1.

0/0 = 1?