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Homer
07-08-2001, 03:41 PM

Define an empty set as x.

Define a full set as y.

Begin.

Definitions above considered, you cannot have less than x.

Definitions above considered, you cannot have more than y.

How can one make a claim that a number less than x may exist by deny a claim that a number greater than y may exist?

If a number is less than x it would be -y because it is given that all numbers less than x are the negative counterpart of a number of equal magnitude that is greater than x.

If a number is greater than y it would be -x because it is given that all numbers greater than y are the negative counterpart of a number of equal magnitude that is greater than y.

-x, -y, x, y, -x, -y, repeat ad infinitum.

Is this wrong?

--Tim

JS Princeton
07-08-2001, 06:54 PM
You can't have it both ways.

Either you are dealing with sets or numbers... those are two different things.

What we're dealing with is a concept of closed and open sets.

Is the set of sets that contain x and y open or closed?

If it's closed then it's closed and your argument makes no sense.

If it's open then it's open and your definitions need to be qualified.

See, numbers and sets aren't necessarily the same thing!

Homer
07-08-2001, 08:52 PM
What is this? This wasn't supposed to be! The OP is a jumbled mess of not much sense.

Could a mod please lock or delete this thread? It wasn't supposed to be posted. It is the thread from Planet 9!

Sorry for the confusion, JS Princeton. This thread was a mistake, the OP wasn't even half finished, organized, or even sensical.

--Tim