Conversation started Jun 21, 2013 at 13:00.
vvavepacket
vvavepacket
Jun 21, 2013 13:00
Hi all, what is the cardinality of the set of Natural numbers, is it 'infinity' or 'undefined'?
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket It's $\aleph_0$.
vvavepacket
vvavepacket
@whats that N shaped thingy
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket The aleph \aleph
vvavepacket
vvavepacket
i see
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket But the definition of such concept seems to be kinda deep.
What set theory book are you reading?
vvavepacket
vvavepacket
Jun 21, 2013 13:08
How to Think Like a Mathematician - A Companion to Undergraduate Mathematics
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket Is it a ST book?
I mean, having a ST chapter in the beginning does not make it a ST book.
Almost every math book has a chapter on ST or Logic.
vvavepacket
vvavepacket
No.
whats aleph
what does it do
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket I'll give you a noobish definiton. Do not trust it fully, I dont trust my mathematical knowledge.
vvavepacket
vvavepacket
ok..
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket The cardinality for infinite sets deals with a connection: Is it possible to enlist every number of an infinite set?
That means that for every number in a set, there is a 1 to 1 correspondence with the natural numbers.
For example:
vvavepacket
vvavepacket
Jun 21, 2013 13:14
Is it possible to enlist every number of an infinite set? ->> I think yes. Just list every number
Bandeira Gustavo
Bandeira Gustavo
$$\begin{matrix}
{1}&{2}&{3}&{4}&{5}&{6}&{7}&{8}&{9}&{...}\\
{2}&{4}&{6}&{8}&{10}&{12}&{14}&{16}&{18}&{...}
\end{matrix}
$$
@vvavepacket Yes. But that is only true up to $\mathbb{Q}$.
vvavepacket
vvavepacket
whats with the matrix
Bandeira Gustavo
Bandeira Gustavo
There is a proof called diagonal argument that shows that such a correspondence can not be made for the set of real numbers.
vvavepacket
vvavepacket
the first row represents the natural numbers
and the second row represents a set of it
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket The matrix shows a correspondence between the naturals and the even numbers.
vvavepacket
vvavepacket
Jun 21, 2013 13:16
ohhh
ok
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket Did you get it?
vvavepacket
vvavepacket
no
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket What are you missing/not understanding?
vvavepacket
vvavepacket
I'm trying to figure out whats missing
@Bandeira, Ill get back to this later. Thanks
Bandeira Gustavo
Bandeira Gustavo
@vvavepacket You're welcome. =)
 
Conversation ended Jun 21, 2013 at 13:22.