Re: Question Regarding the Definition of Cantor's Set


David C. Ullrich wrote:
A = { x : x in A } <-> B = { x : x in C } and C = { x : x in B }

I have no idea whether this is perfectly legal or not, because
I can't tell what you mean. What's given there, and what are
you supposedly defining?


Oops:

A = { x : x in A } <-> A = { x : x in B } and B = { x : x in A }

so that

A = A <-> A = B and B = A

Since the right hand side has two sets, neither of which contain
themselves, it would seem these are legal.

Another way to set it up is:

A = { x : x in A } <-> A = { x : x in f } where f is a constant
function such that f=A.

Again, the right side looks legal.

It seems to me there was a reason for preventing a set from being
defined in terms of itself. That reason may be to prevent loops. But if
you allow loops to be generated indirectly then the original purpose
has been defeated - so why restrict it anymore?

.

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