Recent content by UOAMCBURGER

Homework Statement Problem given to me for an assignment in a math course. Haven't learned about roots of unity at all though. Finding this problem super tricky any help would be appreciated. Screenshot of problem below. [/B] Homework Equations Unsure of relevant equations The Attempt at...

oh yes i do. Update: I used L'Hospital's Rule to find that the sequence converges to 2. But now separating the logarithms you get 2+ln(n^2)/3+ln(n), so would that change my answer I get using L'Hospital's rule? or can i assume an converges to 2 and then use the definition with L = 2?

Homework Statement Homework Equations epsilon - N definition of convergence [/B]The Attempt at a Solution Not sure how to determine whether this sequence converges or not. Thought it could have something to do with the fact that e^2 and e^3 are just constants, so when n > infinity those e...

Don't worry, I learned how to solve it now. since you can find the projection matrix pretty easily then you just plug in the values from the given vector, here W (unit vector of v) the squares cancel the square roots and you're left with that matrix in solution P. But i was wondering how do you...

Homework Statement [/B]Homework EquationsThe Attempt at a Solution The solution is obviously given, but I don't really understand what is done there. What method is being used? so I can understand, because i see how they attained v, but then that vector normalised is not correct is it?

Homework Statement given the matrix https://scontent.fhlz2-1.fna.fbcdn.net/v/t1.15752-9/40882602_313421129235428_2500668957757800448_n.png?_nc_cat=0&oh=7f5d6372c263996c6a11969b072d1349&oe=5BF8F2B7 in RREF we see solution to this system is x1+x2+x3 = 0 in the textbook it says which solutions...

I think my definition was correct, I meant given two elements in the domain (hence x,y ∈ A) then f(x) != f(y) (meaning that no two elements in A can map to the same element in the codomain, B) .. the definition of injective functions. the x !=y just means that the two elements in the domain...

Right, but I don't understand what you mean in post #6. What is clear to me so far is this: For any n ∈ Z, n can be written in the following way, n = x*y + r, where x,y,r ∈ Z also. Now given (in this example) that n != 4q+1 and n != 4q+3, (this is where I'm confused), Why wouldn't it follow...

That doesn't really make sense to me. Can any number in Z, (since that is what we are working with), be represented by 4q+x : x,z ∈ Z? Because it is for n ∈ Z.

Homework Statement Let A, B, C be finite sets such that A and B have the same number of elements, that is, |A| = |B|. Let f : A → B and g : B → C be functions. (a) Suppose f is one-to-one. Show that f is onto. (b) Suppose g ◦ f is one-to-one. Show that g is one-to-one.Homework EquationsThe...

0,2,4,8,12,16,... so on right?

yes i understand that, its just applying De Morgan's laws. But why does that imply that n=4q or n = 4q+2 ONLY? on the answer page it says "since n≠4q+1∧n≠4q+3, it follows that n = 4t or 4t + 2 for some t ∈ Z." My question is why do they say it follows that, that is the case? because how do we...

Homework Statement For any integer n, let A(n) be the statement: “If n 2 = 4k + 1 for some k ∈ Z, then n = 4q + 1 or 4q + 3 for some q ∈ Z.” Use proof by contradiction to show that A(n) is true for all n ∈ Z.The Attempt at a Solution [/B] the answer sheet says that since n !=4q+1 and n !=...

yes its meant to be n2, and obviously I did NOT intentionally write it as n 2 ...

oh that is why i was getting confused, because given statement A>B for a proof by contradiction you get A>~B and show some contradiction, hence my question about the order of the proof. I see what I've done, thanks.