Le 03.03.2013 23:10, WM a écrit : > On 3 Mrz., 22:19, Virgil <vir...@ligriv.com> wrote: ... >> The integers 0,1 and 2 can form a field if the arithmetic is that of >> integers modulo 3. >> >> Note that whether a set of objects forms a field or not depends only on >> how the relevant operations of addition and multiplication are defined >> on the objects of that set, not on what the members of that set are in >> other contexts. > > And the multiplicative inverse is not required? > Ever heard of a ring without rang and rung?
Your are teaching math, or teaching something you pretend to be math, and you do not know that Z/3Z aka Z_3 is a field ? As a matter of fact, for every prime p, and n>1 their is a field with p^n elements.
Oh dear... This is even worse than I thought...
In Z_3, disgusting stupid demented wanna-be mathematician, even a eight year old child would notice that:
1*1 = 1 2*2 = 1
So every non-null element has a multiplicative inverse.
No question you have issues with infinity when you cannot handle the three-elements field...