Math Forum Discussions

Scott Berg

Posts: 1,260
Registered: 12/12/04

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

Plain Text

"netzweltler" <reinhard_fischer@arcor.de> wrote in message
news:917af971-68cf-4e39-a887-d74e78da4dc0@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.