NUS ppl lip lai - Part 4

Status
Not open for further replies.

Death4ngel

Arch-Supremacy Member
Joined
Sep 13, 2008
Messages
10,919
Reaction score
0
How to prove

Proposition 6. The set Z is countably in finite.

Proposition 8. The set Q is countably infinite.

Am I suppose to explicitly define the function? What if I am not supposed to?
 

fzhfzh

Arch-Supremacy Member
Joined
May 27, 2008
Messages
11,599
Reaction score
1,017
wtf still cannot use exchange.nus.edu.sg

simi ********

**** la :mad:

I very dulan with outlook already... just because NUS email down and it cannot access it, it won't even startup for my other email accounts...
 

yoshi_fanboy

Supremacy Member
Joined
Apr 21, 2010
Messages
5,006
Reaction score
0
How to prove

Proposition 6. The set Z is countably in finite.

Proposition 8. The set Q is countably infinite.

Am I suppose to explicitly define the function? What if I am not supposed to?

As far as I know of, for the set of integers, I can't think of a way to prove that the set of integers is countably infinite, without explicitly defining a bijection between the set of natural numbers and the set of integers.

However, for the rational numbers, you could show that there is an injection from the set of rational numbers Q to the set ZxZ. Then ZxZ is equipotent to NxN, which in turn is equipotent to N itself. To show the last statement, consider the function f: NxN -> N, given by f(m,n)=(m+n-2)(m+n-1)/2+m.
Then f is a bijection. So there exists an injection from Q to N, so Q is countably infinite.

So in one way or another, you do need to define a bijection from N to Q, or an injection from Q to N, or a surjection from N to Q somehow.
 

yoshi_fanboy

Supremacy Member
Joined
Apr 21, 2010
Messages
5,006
Reaction score
0
Anyway, MA2108S is not a course on set theory, so you do not need to worry about that lol.
 

SoriyaGTR34

Supremacy Member
Joined
Dec 12, 2009
Messages
6,479
Reaction score
10
tmd, the website give me false hope that can login to nus mail...end up also cannot...
 
Status
Not open for further replies.
Important Forum Advisory Note
This forum is moderated by volunteer moderators who will react only to members' feedback on posts. Moderators are not employees or representatives of HWZ. Forum members and moderators are responsible for their own posts.

Please refer to our Community Guidelines and Standards, Terms of Service and Member T&Cs for more information.
Top