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...
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...
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...
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...