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Topic: Countably Infinite Sets
Replies: 7   Last Post: Dec 29, 2012 12:45 PM

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 Scott Berg Posts: 2,111 Registered: 12/12/04
Re: Countably Infinite Sets
Posted: Dec 29, 2012 12:45 PM

"netzweltler" <reinhard_fischer@arcor.de> wrote in message
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.

Date Subject Author
12/28/12 James Waldby
12/28/12 netzweltler
12/28/12 Virgil
12/28/12 James Waldby
12/29/12 netzweltler
12/29/12 Scott Berg