Rufus
March 24, 2010, 8:49pm
41
Warrior_s_Dreams:
Yes, this is the set of elements in Z_4 with respect to addition modulo 4. It’s actually a bit of a notational confusion, but Z_4 = {0, 1, 2, 3} really means {[0], [1], [2] ,[3]}. Then we have [2] + [2] = [4] = [0] modulo 4 since these are equivalence classes…
To elaborate little, people usually consider the elements of Z_4 to be equivalence classes of integers.
If you think of the elements of Z_4 as ‘0-3 with special rules’ then ‘4’ obviously doesn’t make sense.
Coth_X
March 24, 2010, 9:10pm
42
Rufus:
To elaborate little, people usually consider the elements of Z_4 to be equivalence classes of integers.
If you think of the elements of Z_4 as ‘0-3 with special rules’ then ‘4’ obviously doesn’t make sense.
I haven’t got to rings, but my teacher basically taught us that 4 technically isn’t in the set, but I see what you mean by equivalence.
@warrior , are you referring to relatively prime? Or a different concept?
Rufus
March 24, 2010, 9:53pm
43
Coth_X:
I haven’t got to rings, but my teacher basically taught us that 4 technically isn’t in the set, but I see what you mean by equivalence.
@warrior , are you referring to relatively prime? Or a different concept?
In the sense that you’re used to “0” isn’t part of Z_4 either.
Regarding primes…http://mathworld.wolfram.com/PrimeNumber.html http://mathworld.wolfram.com/PrimeElement.html