netzweltler
Posts:
280
From:
Germany
Registered:
8/6/10


Re: Countably Infinite Sets
Posted:
Dec 28, 2012 5:16 PM


On 28 Dez., 21:53, James Waldby <n...@valid.invalid> wrote: > On Fri, 28 Dec 2012 12:51:29 0600, fasnsto wrote: > > "netzweltler" <reinhard_fisc...@arcor.de> wrote ... > >> Does the set {{1}, {1,2}, {1,2,3}, ...} contain all natural numbers? > > > no, it would contain the set of all natural numbers. > > Let S = {{1}, {1,2}, {1,2,3}, ...}. The infinite union of the members > of S would be a set containing all natural numbers, but no member of S > is itself a set containing all natural numbers. Of course, as noted in > some earlier replies, S is isomorphic to the naturals. > >  > jiw
I understand, that the union of the members of S contains all natural numbers. But, did I really write the union here? {{1}, {1,2}, {1,2,3}, ...}
Isn't it a list of infinitely many rows like
1 1,2 1,2,3 ...
Does the list contain all natural numbers? Is this list an union?

