Re: Question

Virgil <vmhjr2@xxxxxxxxxxx> wrote:
In article <1146420387.565174.229030@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"zuhair" <zaljohar@xxxxxxxxx> wrote:

Divide that number by itself will only result in itself, since it is
infinite?!

Zuhair

Any number that it is possible to divide by, divided by itself had
better be equal to 1, or all of mathematics will collapse.

Virgil, I didn't think you were prone to hyperbole.

It depends, among other things, on what you mean by "number". In interval
arithmetic, an interval is sometimes considered to be an "interval number".
Let's consider an example in which an interval number is divided by itself:

[1,2] / [1,2] = [1/2,2]

Hmm. I don't think anything collapsed. (Perhaps you'd have liked the answer
to have "collapsed" to the degenerate interval number [1,1]. But at least
the correct answer does _contain_ 1.)

Zuhair claims to have "numbers" x such that x/x = x.

In the reals, the only such number is x = 1, of course. But there are
systems (such as wheels) in which an element, other than 1, divided by
itself can yield that same element. Of course, whether you want to call
such an element a "number" is a different matter.

Regards,
David
.

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