Double post... Doesn't have the option to delete...
Last edited by Afaceinthematrix on Tue Oct 27, 2009 12:38 am; edited 2 times in total
Hmmmm... I'm going to have to think about this for a while.
Can you tell me if I'm starting off correct?
I think we'll have to define a set that's a subset of the natural numbers. We can then show that it forms an injection with the set containing the natural numbers which means that the set is countable.
We then need to show that this set contains the empty set. *axiom*
We then need to find a way to show that every element in the set has a successor.
From this, we may be able to define "1" by somehow showing that it's a successor of the empty set?
Maybe I need to visit the TA or professor's office hours for my set theory class... If you can confirm that I am at least headed in the right direction, then I'll put some more effort into it and then visit office hours... I hate visiting a professor empty handed or when I'm in the completely wrong direction...
We standardized the symbol "1" as the number one. The first natural number.
Then people said, hey what if we put together two 1's? And so, they invented addition.
So any number greater than 1 was expressed as 1+1, 1+1+1, 1+1+1+1, ... But those lazy people just thought: hey, why don't we shorten it? Maybe we could use the symbol "2" to denote 1+1, and "3" to denote 1+1+1, and so on.
And it deemed to be practical. And everyone lived happily ever after.
Well it's easy.
We define the natural numbers. We define addition and multiplication. We define 1 as (for example) the identity of multiplication. We know 1+1 exists, because this is one of the axioms of addition in N. We define 2 as 1+1.
), what do we mean by "1", "2" and "+"?
