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Topic: Two Finite Arithmetics
Replies: 19   Last Post: Apr 9, 2014 9:27 PM

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Dan Christensen

Posts: 2,438
Registered: 7/9/08
Re: Two Finite Arithmetics
Posted: Apr 8, 2014 4:35 PM
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On Tuesday, April 8, 2014 2:08:49 PM UTC-4, Dan Christensen wrote:

> You might start by proving the associativity and commutativity of + and * as you have defined them.

Better still, as a kind of shakedown cruise, show that (in your notation) the following conditions satisfy your axioms:

N = {0,m}
0 =/= m
S0 = m
Sm = m
0+0=0
0+m=m
m+0=0
m+m=m
0*0=0
0*m=0
m*0=0
m*m=m

Dan
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