 Originally Posted by Xei
The number 0 is defined as those sets which can be put into a one-to-one mapping with {}, or '∅', the set of no elements
 Originally Posted by tempusername
This definition seems pretty meaningless and if anything is a contradiction.
 Originally Posted by Xei
I don't see how it's either. You can use it to make distinctions; therefore it isn't meaningless.
Distinctions denote meaning
Distinctions denote meaning
Distinctions denote meaning
OP CONFIRMED NIHILISM FETISHIST
DO YOU HEAR THAT, OP? YOU AND YOUR FRANK N. WILEY ARE FETISHISTS OF NIHILISM. YOU HAVE A BONER FOR MEANINGLESSNESS
But wait...
Stuff only becomes worth talking about when we have non-empty and/or infinite sets.
SO, OP, NOT ONLY IS YOUR WISH TO UNITE NOTHING WITH EVERYTHING A REFLECTION OF YOUR OBSESSION WITH MEANINGLESSNESS, THE CONCEPTS YOU'RE CONCERNED WITH IN THE FIRST PLACE (NOTHING AND INFINITY) ARE ALSO TOTALLY WORTHLESS! SUCKS TO SUCK
But hey, we just went full circle thanks to Xei calling an empty set worthless, so I guess OP wins in the end. Lel (full circle, get it?)
Or are you implying worthiness doesn't correlate to meaning, Zei?
And one more question, just to clarify some math:
A map which sends the empty set to some other set does therefore meet the demands of the definition, although vacuously so; there are no elements in the set, so trivially the map sends 'all of the elements' in the set to some element elsewhere.
Are you telling me that anything, even the concept of zero, even "nothing," mathematically falls into a set?!
Counting is about the sizes of sets.
Size... d-do sets even truly have the property of size? Any property of a set is defined by the elements which it holds... So:
Counting is about the sizes of sets.
Sizing sets is about maps.
Mapping is about distinguishing elements.
Numbers distinguish.
And the only thing to do with numbers is count them... f-f-full circle...
 Originally Posted by Xei
[When counting] we are not interested in what is actually inside the sets; we are trying to abstract the 'number' of elements from the set without considering anything out about it, in the same way that the number three is abstracted from three sheep and three trees and three rocks.
What is it called mathematically when we're not considering the number of elements but trying to distinguish them from one another based on their properties like color or shape, real or fake?
Isn't this method of "abstraction" reproduced outside of counting? Or is everything counting? We have sets and elements which aren't the verb counting obviously. They are nouns but we can't distinguish a set from another set or one element from another element (make a noun essentially) without counting. Same goes for distinguishing elements from sets, right? But what about things like fucking brackets {}, equal signs and all those non-numerical symbols mathematical equations require?
C = { red, green, blue }
How would we show the above equation using math alone without falling into an infinite mapping sequence to distinguish each element as a standalone ... uh number instead of a word?
And isn't it impossible for an element to standalone in the sense that other elements distinguish its ... uh ... distinctness?
FUCK I SUCK AT MATH
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