Re: LOGO-L> ToonTalk versus MicroWorlds

[yehuda <yehuka@softhome.net>]

Bill Kerr wrote:

<snip>

> Oh dear, that drags up a dim memory from my neglected
> mathematical past!
> Please tell me why 0!=1. I can't remember if I've forgotten or maybe
> I never
> knew! mmm .... would that come out correctly in the ToonTalk version,
> must
> try it?
Hi Bill,

0! is defined as 1 because:

    (a)    1!=1, correct?

But also, by definition,: n!=n*(n-1)!, so

    (b)    1!=1*0!

If a=b and a=c you conclude that b=c, so from (a) and (b) you come to:

    (c)    1=1*0!

What you multiply by 1 to get 1? 1 of course, so it's justified to define 0! as 1.

Regards and a merry xmas,

Yehuda

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http://www.geocities.com/CollegePark/lab/2276/
e-mail: yehuka@softhome.net
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