Recent content by Temp0

Ohh, i didn't know that mattered, I'll keep that in mind for all future proofs, I think i have the right idea now, i'll just put it onto paper and see if I can solve it and the other problems. Thank you very much for all the assistance!

Hmm it's kind of hard because my induction hypothesis came from my notes where the general idea was to assume that everything within the range of the lower boundary to the upper boundary (k) is assumed to be true, and then I needed to prove that the equation works for k + 1 in my induction step...

Ohh, I see! Yup, my professor usually writes it like that so I guess I copied him, it does make sense, there is always a larger number so I guess it's pointless to assume there to be a larger one.

Hmm, I see, but don't I say that at the end when I put 3 ≤ m ≤ k ?

Hmm I'm not sure, I don't think I've ever learned that yet, and I'm trying to figure it out now. So far, what I know about the boundaries of floors is this: If x is some real number, and the floor of x is n, then n ≤ x < n+1 Also, could you clarify on how my induction hypothesis is bad...

Homework Statement are[/B] an = afloor(n-2) + afloor(2n/3) + n a0 = 1 Prove that for all n ≥ 3, an > 4n Homework EquationsThe Attempt at a Solution Since this is induction, I start out with a base case: Base Case (n = 3): a3 = a1 + a2 + 3 = 3 + 8 + 3 = 14 4(n) = 4(3) = 12 14 > 12 Therefore, the...

I see... I guess I missed that part, haha, just wondering, does it come from the inequality: floor (2x) <= 2x < floor(2x) + 1 ? I can see how it relates... kind of, since 2 floor (x) <= 2x as well, but how does 2floor(x) <= floor (2x) ?

Homework Statement Prove that for any real number x, if x - floor(x) < 1/2, then floor(2x) = 2 floor(x) Homework EquationsThe Attempt at a Solution Assuming that x is a real number. Suppose that x - floor(x) < 1/2 Multiplying both sides by 2, 2x < 2 floor(x) + 1 from the definition, 2 floor(x)...

Ohh, I see, thank you so much for your help.

Ohh, so you're saying that m would be like a constant value, whereas in the other case it could be a variable? How exactly does the order play into this?

Homework Statement There exists a number m, which is an element of the positive integers, that for all positive integers n, n+m can be divided by 3. Prove whether this statement is true or false. Homework EquationsThe Attempt at a Solution I ran into a similar question earlier on, which just...

Hmm yes, I solved it somewhat anyway, well, that is to say I got the right answer but I'm going to have to study over the method some more so I can see what happened here. Thanks for all your assistance.

Still kind of confused on where to put the t-v, so am I taking the integral of f(t-v)? Well, I may come across it in the future, but I'm studying engineering so I might not get into that level of physics.

Okay so this is just going off what I'm reading off the internet right now... I know the inverse LT of G(s) is e^(-t)... Then I use an arbitrary f(t) to denote the inverse LT of F(s) I replace t with a temporary variable v, and determine a definite integral from 0 to t. \int^t_0...

Wow, I never learned about this, but after looking around for a while I found the convolution theorem that says the inverse transform of G(s) and F(s) is just (f*g)(t)