Tilted Forum Project Discussion Community - View Single Post

kel · 12-18-2003, 02:42 PM

Well the sets are identical... one is a synonym of the other through substitution...
The formal way to prove this is if you take the opposite of union (I forgot the formal name for this operation) of the two sets then it should the empty set. This means they are equivalent (I don't know what conformally equivalent is).
As I will show, if you mess with R, or r then you won't get the empty set.

The basic deal is that if R is not equal to infinite, but to some finite number, then the set will always be of a finite size in the positive direction.... So it could never be equal to the inifinite positive set and when you take ~union (the set of all elements that exists on only one set or the other, but not in both) of the two you will not have an empty set. If it is -infinite then you will have an empty set. Whether r is infinite or not makes no difference, I am not sure but in this case if r were infinite or -infinite we would get the empty set, which ~union with the original, is non empty.

If little r were set to anything other then zero then then again the set's ~union would have elements in it, either elements <0, or elements >0.

That basically takes care of the two cases I see here... r != 0, or R != infinity

Don't know if this proof holds water in the crazy set universe.

12-18-2003, 02:42 PM	#4 (permalink)
kel WARNING: FLAMMABLE Location: Ask Acetylene	Well the sets are identical... one is a synonym of the other through substitution... The formal way to prove this is if you take the opposite of union (I forgot the formal name for this operation) of the two sets then it should the empty set. This means they are equivalent (I don't know what conformally equivalent is). As I will show, if you mess with R, or r then you won't get the empty set. The basic deal is that if R is not equal to infinite, but to some finite number, then the set will always be of a finite size in the positive direction.... So it could never be equal to the inifinite positive set and when you take ~union (the set of all elements that exists on only one set or the other, but not in both) of the two you will not have an empty set. If it is -infinite then you will have an empty set. Whether r is infinite or not makes no difference, I am not sure but in this case if r were infinite or -infinite we would get the empty set, which ~union with the original, is non empty. If little r were set to anything other then zero then then again the set's ~union would have elements in it, either elements <0, or elements >0. That basically takes care of the two cases I see here... r != 0, or R != infinity Don't know if this proof holds water in the crazy set universe. __________________ "It better be funny" Last edited by kel; 12-18-2003 at 02:52 PM..