ø = {ø}

Sal1981 · Posted: Mon Mar 24, 2008 12:23 pm Post subject: ø = {ø}

I know I lack the Number Theory, but bear with me.

This is only preliminary, so take it with a grain of salt.

Basically it's about a new math theory.

If you understand then 0 (Zero) is actually not a number, but the lack of a number. Which is why you can have a Zero-Set that is: 0 = {0,0,0, ... , 0} as well.

The <0> simply means "right and/or wrong follows as ..."
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Chaoslord2004 · Posted: Sat Aug 09, 2008 11:40 am Post subject:

I'm not sure I entirely understand your new mathematical idea, but I do know in adopting it, one would have to through up basic set theoretic notions. Most importantly, the notion that 0 is the empty set, and then building numbers up from there:

0 = []

1 = [[]]

2 = [[[]]]

3 = [[[[]]]]
.
.
.
.

This seems like an intuitively bad idea, since set theory forms the basis for mathematics. All discussion of mathematics can be reduced to talking about set membership and its relations to subsets.
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Knight_of_BAAWA · Posted: Mon Aug 11, 2008 10:56 pm Post subject:

*doesn't want to be reminded of the 8-page proofs demonstrating that something is an abelian group*
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Chaoslord2004 · Posted: Mon Aug 11, 2008 10:59 pm Post subject:

Dragonfall · Intern Joined: 08 Apr 2007 Posts: 53 Local time: 7:42 PM

I haven't posted here for a while so I might be digging up old threads.

What you described in your title, x={x} (the empty set is not equal to the set containing the empty set, so I assume you're using that symbol as a variable), is what mathematicians call "non-well-founded sets". In standard set theory all sets are well-founded, which in practice means that they don't contain themselves, and they don't contain an infinite downward chain of sets containing sets. Non-well-founded sets are studied on the fringes of mathematics because pretty much everything there is to know about them is known. I suggest reading "Non-Well-Founded Sets" by Peter Aczel.

jaycorath · Posted: Mon Sep 01, 2008 3:30 am Post subject:

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