> > Now suppose (a,b)=(c,d), that is,
> > {{a},{a,b}}={{c},{c,d}}. Either {a}={c} or
> > {a}={c,d}, both of which imply that c=a.
> I assume you mean that, out of {c} or {c,d},
> {a} = {c} is the only valid choice, as {a} = {c,d}
> leads to the contradiction {c,d} = {c}.
No, that's not what I meant. In fact, {c,d} = {c} is not a contradiction, it merely implies that d = c.
What I meant was that c is an element of the right-hand side (whether that is {c} or {c,d}), and therefore it must be an element of the left-hand side, and therefore it must be a. |
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