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Old 11-03-2012, 04:27 PM   #706
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wtf still cannot use exchange.nus.edu.sg

simi lan jiao

fark la
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...
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Old 11-03-2012, 04:50 PM   #707
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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.
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Old 11-03-2012, 04:51 PM   #708
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Anyway, MA2108S is not a course on set theory, so you do not need to worry about that lol.
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Old 11-03-2012, 06:00 PM   #709
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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...
fark microsoft
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Old 11-03-2012, 06:05 PM   #710
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tmd, the website give me false hope that can login to nus mail...end up also cannot...
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Old 11-03-2012, 06:11 PM   #711
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eh people, can use liao...
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Old 11-03-2012, 06:22 PM   #712
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up and running!
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Old 11-03-2012, 06:30 PM   #713
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heng smooth liao,
if not cannot summit report then die
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Old 11-03-2012, 09:07 PM   #714
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Anyone taking special sem? Want take with me?
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Old 11-03-2012, 09:46 PM   #715
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Anyway, MA2108S is not a course on set theory, so you do not need to worry about that lol.
Later mid terms come out sets and counting then hong gan sia!
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Old 11-03-2012, 09:49 PM   #716
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Anyone taking special sem? Want take with me?
you sponsor ?
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Old 11-03-2012, 09:51 PM   #717
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what is MIT ?
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Old 11-03-2012, 10:10 PM   #718
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MIT >.< so lucky. Jealous.
It's not luck, it's 実力.
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Old 11-03-2012, 10:17 PM   #719
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sian, BRDF equation makes my head spin...
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Old 11-03-2012, 10:19 PM   #720
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moi ma1312 mid-term get 30+ nia












Moi MA1521 mid term last sem i got 34
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