
Re: Countably Infinite Sets
Posted:
Dec 29, 2012 12:45 PM


"netzweltler" <reinhard_fischer@arcor.de> wrote in message news:917af97168cf4e39a887d74e78da4dc0@c14g2000vbd.googlegroups.com... On 29 Dez., 00:58, James Waldby <n...@valid.invalid> wrote:
<snip>
>I guess what I am heading for is the ultimate abuse of set notation >then:
>1 >1,2 >1,2,3 >...
>Since I can see the set of natural numbers infinitely many times >represented in the diagonals of this list I would reorder the elements >of this list and write
>{{1}, {1,2}, {1,2,3}, ...} = {{1,2,3,...}, {1,2,3,...}, >{1,2,3,...}, ...}
>in set notation then. Doesn't make sense at all, does it?
nope, they are not equal at all. the first set, >{{1}, {1,2}, {1,2,3}, ...} , contains the set with 1 and no other elements. which the second set, {{1,2,3,...}, {1,2,3,...}, does not contain.

