Re: .999... ?= 1

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 06/09/04 

Date: Wed, 09 Jun 2004 07:56:24 +0100

Eckard Blumschein wrote:

> *** T. Winter wrote:
>
>> Depends on what you define as a number (I have not seen a definition in
>> this thread yet),
>
> Being a layman, I looked for such definition and was disappointed, too.

You won't find a definition of a number: you will find definitions
of real numbers, rational numbers and complex numbers. It is a historical
accident that, for instance, the complexes are regarded as "numbers"
but the quaternions usually are not.

>
> I naively imagine the reciplocal of a number might be related to but not
> the same as the reciprocal of a function or a graph.

category mistake: functions have (well they usually don't) inverses,
not reciprocals.

> I also wonder why Fourier transform of a continuous periodic function
> (aleph2) consists of dicrete values (aleph1) and vice versa no matter
> whether or not it is compex-valued.

If one wish to take Fourier transforms of periodic functions one
needs to work within the space of tempered distributions.

> I merely found this within at least one book on Cauchy(?) written as or
> more likely based on a thesis by an outsider. Don't ask me which one.
> Also I was told that zero is not necessarily a number, and if I recall
> correctly, I found that zero is the only infinitesimal within the
> hyperreal numbers.

You probably don't (it's not true). 

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9"
Francis Wheen, _How Mumbo-Jumbo Conquered the World_