A use for integer quotients

[Stephen Horne]

On Wed, 25 Jul 2001 22:28:14 +0100, Gareth.McCaughan at pobox.com (Gareth
McCaughan) wrote:

>By the way, any definition of "mathematician" that excludes
>pure mathematicians is spectacularly broken.

What about a definition that generalises to include *more* than just
pure mathematicians? It is you who is narrowing the definition, not
me.

I never once claimed that integer division was allowed in all
mathematics. I claimed it existed in mathematics. I specifically
pointed out that it was generally done-and-dusted and therefore not
something of interest to current academics - but that it did survive
in everyday life. After all, would you really share five TVs between
two people by turning the fifth TV into junk? Or would you perhaps
treat it as a remainder?

Others claimed 'the methods I use do not allow this, and the methods I
use are part of mathematics, therefore mathematics doesn't allow
this'. As a mathematician, you *should* recognise this as a false
syllogism. Or perhaps you consider that logic - being outside your
particular field - doesn't exist?

Mathematics includes many ideas that are not applicable to pure
mathematics - applied mathematics presumably contains many such ideas.
The fact that they do not apply in specifically in current pure
mathematical study does not mean they aren't a part of mathematics.