On Sun, 20 Jul 2008 19:50:56 +0100, Jack <jj@[EMAIL PROTECTED]
>
wrote in <news:hOLgk.14342$9S6.835@[EMAIL PROTECTED]
> in
alt.algebra.help:
> "Brian M. Scott" <b.scott@[EMAIL PROTECTED]
> wrote in message
> news:1usfqoaxp7374.gz6czvua09cx.dlg@[EMAIL PROTECTED]
>> On Sat, 19 Jul 2008 22:58:04 +0100, Jack <jj@[EMAIL PROTECTED]
>
>> wrote in <news:trtgk.39540$7B3.5025@[EMAIL PROTECTED]
> in
>> alt.algebra.help:
>> [...]
>>> The thing that perplexes me a little is that Paul was
>>> saying I could define |N as the set of positive integers
>>> if I so wished, which might in retrospect turn out to
>>> be a good option for me; but then if we have t: |N --> |N
>>> you allow me to have t(n)=0, but 0 is not positive.
>> I don't see how this relates to what preceded it.
> It's just something that niggles me: if you have a
> function t: N ---> N and N is by definition a positive
> integer,
Obviously it isn't. Presumably you mean 'and N is by
definition the set of positive integers'.
> it looks wrong to refer to t(n)=0;
Of course it's wrong!
> yet neither you nor Paul objected to the use of N --->N
> when N could, so it seemed, be the set of positive
> integers.
Paul will have to speak for himself, but *I* have all along
used 'N' only to denote the set of non-negative integers.
> So if I then say t: Z^+ ---> Z^+, and refer to t(n)=0, is
> that sound or unsound?
It's obvious nonsense.
|
