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If something is associative, then for example $(x + y) + z = x + (y + z)$ is true. I also know that in general subtraction is not an associative operation, but what if subtraction is applied to $\lbrace 0 \rbrace$. Is subtraction an associative operation then? Since $0-0=0-0$.

user6259845
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  • A single example is not enough. Yes, subtraction is associative on the set containing {0} and nothing else. But that is a (literally) trivial case. To state that "subtraction is associative" then it is associative for ALL $a,b,c$ and not just one special case. – fleablood Oct 16 '17 at 02:24

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Yes, Subtraction is associative on $\{0\}$..

But that is a trivial case. Less trivial subtraction is also associative on $\mathbb Z_2 =\{0,1| 0+1=1+0 = 1; 0+0 = 0; 1+1 = 0\}$ (because $1 = -1$).

But for any group with at least three elements it is not:

I think.

fleablood
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