Recent content by GreenApple

Is there any PhD Program in US on logic where I can apply as a student with a computer science background and further combine my interest in logic, philosophy, math and computer science? For now, I only know a program at CMU, which is PhD Program in Pure and Applied Logic.

Homework Statement you are in a land inhabinated by people who either always tell the truth or always tell falsehoods. You come to a fork in the road and you need to know which fork leads to the capital. There is a local resident there, but he has time only to reply to one yes-or-no...

the first problem : M is a 2n*2n matrix in the form A B C D where each block A(at the position 1,1) B(1,2) C(2,1) D(2,2) is an n*n block. A is invertible and AC=CA. Prove the det M = det (AD - CB) the second problem: A is an n*n matrix with integer entries. Prove that the inverse of A...

Can anyone give me some hint on proving 1.3 13 and 1.5 3 of Algebra by Artin?

Truth? Inner peace? I don't know what I want. My life sucks!

Probability and Statistics is required by my major, which is software engineering! I am taking that course right now and I don't like it at all, for the sake of the material itself, not the teacher. I tried but could not like it. Though I love algebra and analysis. I have here too many...

I am always gratefull for all your help. I got this sentence from a dictionary: Clarke says his team could have lasted another 15 days before fatigue would have begun to take a toll. I am just wondering why it was not this sentence : Clarke says his team could last another 15 days before...

Another question: What am I suppose to say when someone say "whould mind opening the door?" ? Sould I say "sure, no problem" or "no, of cause not" ,provided I want to do the favour?

No, it may be not so obvious to you that g is onto, so let me add somthing. For any m in the set {1,2,...,n-1}, there is a y in A such that f'(y)=m(because f' is onto), but y!=x because f'(x)=n, which leed to that y is in Ax. So for any m in {1,2,...,n-1}, there is a y in Ax such that g(y)=m...

Thanks, professor! That is a beautiful proof. I think my problem is solved. But, I can't help but show some interesting point here. First, I think a set A is finite if and only if there exist some n which we refer to as the size of A, such that "there exist a one to one and onto function...

I have some other questions. What is the difference between the tow sentences "She is pretty, isn't she? " and "She isn't pretty, is she? "?

Thanks, teacher! Your advise always helps! What a stupid mistake I made The right thing to do may be to say "a set A is finite if and only if we can get a one to one function A->S(n) where S(n) is the set { 1, 2, ..., n }, and we can also get a one to one function S(n)->A. And we say that...

Well, you can ask me any question about it. I am glad to help :)

I think it will make some sense to try this way: I assume that a set A is finite if and only if we can get a one to one function A->S(n) where S(n) is the set { 1, 2, ..., n }, and we say that set A is of size n. Since we want to prove that the ONE TO ONE function f(x) A->A is onto, we...

Thanks, I think I got it. :)