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Re: All Integers are Interesting (with Proof)
Posted:
Apr 24, 2005 6:24 PM


Jim Spriggs wrote: > Reef Fish wrote: > > > > ... > > > > Actually, that statement can only be PROVED if the number is an > > INTEGER. > > > > Proof: > > > > We proceed by the method of reductio ad absurdum > > > > Suppose the set U of uninteresting integers is nonempty. Then, since > > You need to say _positive_ integers, else U can be > > {1, 2, 3, 4, ...}
Thank you for your interest in the subject. ;) Yes, U can be any negative integers too. Nothing in the proof below assumes U or u to be positive integers only.
If the smallest "uninteresting integer" is 12345679, or any other negative integer, the proof still holds.
> > > it is a set of integers, there is a least member of U, u, say. u has > > the property of being the smallest uninteresting integer, which is > > interesting  a logical contradiction. Thus we have disproved the > > hypothesis that U is nonempty, hence empty. The set of uninteresting > > integers is empty means there are no uninteresting integers. > > > > QED. > > > >  Bob.
1 is certainly an interesting integer. The square root of 1 takes you from the real domain to the complex domain is just one of the "interesting" facts about it. :)
25,361,761 is interesting because ... according to the Guiness Book ...
The largest slot machine payout is $39,713,982.25 (£25,361,761), won by a 25yearold software engineer (hence 25,361,761 won by the slot machine <g>) from Los Angeles after putting in $100 (£64) in the Megabucks slot machine at the Excalibur HotelCasino (pictured), Las Vegas, Nevada, USA, on March 21, 2003
 Bob.



