Talk:Finite
From Academic Kids
Wait a minute!!
This encyclopedia defines the terms "natural number" and "finite" in terms of each other!!
-- Anon
This isn't Bourbaki; we're not trying to develop a single well-grounded development of mathematics but instead to describe all of the various interrelatinships between mathematical (among other) concepts. So if X can be defined in terms of Y while Y can be defined in terms of X, then both definitions should be included.
That said, any interesting definitions of X or Y that don't mention the other property should also be included! If you have any good ones, then please add them.
-- Toby Bartels 06:46, 25 Sep 2003 (UTC)
I don't agree : even without being Bourbaki, if one definition is given in terms of the other and reciprocally, then it is mathematically completely useless !
Also, if n=0 is a natural number, then is {1,2,3,...,n} the empty set?
In fact, I wanted to know if according to wikipedia, a finite set can be empty (i.e., if the empty set is finite or not).
— MFH: Talk 23:29, 19 Apr 2005 (UTC)
Well, there exists no bijection between the empty set and one of its proper subsets, since there are no proper subsets of the empty set, so by default it is finite. bananaclaw May 5, 2005
