Recent content by toxi

I found it, it was in my lecture notes. now I need a total, surjective, non-injective function from N to Q. Any suggestions? I'm not really good with this, sorry

Apparently cantor's zig zag is the appropriate for this proof

Well as I said, my question is "I need to prove that the product of 2 countable sets is countable"

so, by using cantor's zig zag this is the proof it asks me for ? doesnt this prove just one of the two sides of the rational numbers (i know that Q is in fact the union of negative rationals and positive) ?

I'm a bit stuck here, my question asks me to prove that the product of 2 enumerable sets is indeed enumerable with an argument or a counterexample. I pretty much have no idea on how to proceed, although i know that the product is enumerable

Apparently that's Cantor's zig-zag (which is the one I meant to say in the previous post) Anyway, I found this on the internet http://www.homeschoolmath.net/teaching/rational-numbers-countable.php Do you mean that for instance (r4, r4) or 5,6,7 whatever number it is, is the encoding I've...

Yeah, according to my notes an encoding is "a total injective function C: A->N into the natural numbers. For a in A, the number c(a) is called the code of A" I think I've seen the proof you're talking about, its the one done by Cantor's diagonalization right ?

I know this would probably be in a different category but I wasn't sure. Find an encoding for Q x Q. I have no idea what to do for this question was we weren't even taught encodings. any help is appreciated thanks

I need some help here... I've got the following assignment to do Prove that if M>N then any system of N homogeneous equations in M unknowns has many solutions. I am a bit stuck with this one. I thought about creating a MxN Matrix and to display the determinant with 1's. and then say...

So there are no further steps needed to show? That's what I did actually...

Well that is just the solution I have found. What do you mean that the matrix has the required properties? Do I need to figure out the homogenous equations first? I am a bit confused with all these, I've been reading lecture notes and books for ages but none of them seems to make sense...

Homework Statement Find a linear transformation T from R3 to R3 which has the effect of rotating an object clockwise by angle θ around the x-axis. Homework Equations none The Attempt at a Solution I know that I should work with matrices to show how I came up to the final matrix...