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Topic: All Integers are Interesting (with Proof)
Replies: 1   Last Post: Apr 24, 2005 6:24 PM

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Posts: 2,083
Registered: 2/11/05
Re: All Integers are Interesting (with Proof)
Posted: Apr 24, 2005 6:24 PM
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Jim Spriggs wrote:
> Reef Fish wrote:
> >
> > ...
> >
> > Actually, that statement can only be PROVED if the number is an
> >
> > Proof:
> >
> > We proceed by the method of reductio ad absurdum
> >
> > Suppose the set U of un-interesting integers is non-empty. Then,

> 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 "un-interesting 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
> > the property of being the smallest un-interesting integer, which is
> > interesting --- a logical contradiction. Thus we have disproved

> > hypothesis that U is non-empty, hence empty. The set of
> > integers is empty means there are no un-interesting integers.
> >
> > QED.
> >
> > -- Bob.

-1 is certainly an interesting integer. The square root of -1 takes
from the real domain to the complex domain is just one of the
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
a 25-year-old 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 Hotel-Casino (pictured),
Las Vegas, Nevada, USA, on March 21, 2003

-- Bob.

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