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Topic: Is it possible that 3+4=8?
Replies: 21   Last Post: Jan 29, 2011 9:06 AM

 Messages: [ Previous | Next ]
 Ilmari Karonen Posts: 311 Registered: 2/1/07
Re: Is it possible that 3+4=8?
Posted: Jan 23, 2011 8:47 PM

On 2011-01-23, Ilmari Karonen <usenet2@vyznev.invalid> wrote:
>
> It also turns out that the otherworldly addition as we have defined it
> corresponds in a simple way to ordinary addition. In particular,
>
> x & y = g( f(x) + f(y) ),
>
> where
>
> f(0) = 0, f(o) = 1, f(~o) = -1, f(x) = x+1 and f(~x) = -(x+1)
>
> for all positive integers x, and g is the inverse of f, i.e.
>
> g(0) = 0, g(1) = o, g(-1) = ~o, g(x) = x-1 and g(-x) = ~(1-x)
>
> for all integers x > 1.

Of course, there's a typo here: that should be g(-x) = ~(x-1) for all
x > 1.

--
Ilmari Karonen

Date Subject Author
1/23/11 Craig Feinstein
1/23/11 master1729
1/23/11 LudovicoVan
1/24/11 LudovicoVan
1/24/11 LudovicoVan
1/24/11 Virgil
1/23/11 Ilmari Karonen
1/23/11 Ilmari Karonen
1/23/11 Virgil
1/23/11 Tim Little
1/23/11 Joshua Cranmer
1/24/11 hagman
1/24/11 Joshua Cranmer
1/23/11 Brian Chandler
1/24/11 donstockbauer@hotmail.com
1/24/11 cwldoc
1/24/11 Craig Feinstein
1/24/11 Joshua Cranmer
1/24/11 Craig Feinstein
1/25/11 Hauke Reddmann
1/29/11 Bill Taylor