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)?
On 25 Oct 2002 09:32:48 -0700, vgopa...@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.
> On 25 Oct 2002 09:32:48 -0700, vgopa...@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.
"John Christiansen" <superkae...@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.]
> > >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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> >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.
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.
"John Christiansen" <superkae...@mail1.stofanet.dk> wrote in message <news:3dba7576$0$1010$ba624c82@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.
> > >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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