Recent content by Melodia

Oh ok, then the answer would be obvious right? I mean if both f and g has to be positive, then either f or g has to be smaller than f + g; then they have to be in O(h) as well.

Ok thanks for clearing it up. So basically it's saying: If f(n) + g(n) \leq c[h(n)] Then f(n) \leq c[h(n)] and g(n) \leq c[h(n)] The tricky part is that f(n) could be negative right? Since it says "\forall f". Then f(n) could be larger than (f + g)(n)? Or does "\forall f, g \in F" mean "for...

Homework Statement I'm having trouble understanding this pair of claims: Homework Equations The Attempt at a Solution So g is some function whose result is greater or equal to 0... but I don't really get what the rest of the claim means. Could someone please explain them to...

Oooh I see. Since c is fixed and chosen before the n, then there will always be an n that contradicts the statement right? I'm guessing the same thing applies to this other problem right?

Homework Statement Thanks for the help on the last problem. Here is the final problem set I'm stuck on: Homework Equations The Attempt at a Solution To me it seems that there will always be a positive c so that cg(n) is greater or equal to f(n). No matter how large n is...

Oh because I wanted the indentation to make it look neater.

The example makes sense, however I'm now stuck at the actually proving it part ^^ So far I've got: Assume x is in R and z is in Z By definition of floor of x, [x] <= x Then ([x] + z) <= (x + z) ...(but how do I manipulate ([x] + z) <= (x + z) into [x + z] = [x] +...

Hmm I'm supposed to use the formal method of proving, in this form: Assume x is in R Assume p(x) Then r1(x) Then r2(x) ... Then q(x) Then p(x) ) q(x). # assuming antecedent leads to consequent Then for all x in R, p(x) => q(x) But some general...

Homework Statement Heya everyone, I need help proving or disproving these claims: Homework Equations The Attempt at a Solution This definition of the floor totally confused me, I don't know how to start this problem as I don't recognize anything such as axioms or formulas from...

Thanks! I got it after numerous tests of plugging in numbers.

Homework Statement Hello thanks for everyone who helped me on the previous implication proof, here's another problem I'm stuck on: (Prove or disprove) Homework Equations The Attempt at a Solution I think it has something to do with x^2 - y^2 = (x + y)(x - y), and here's my...

Oh sorry I changed to quote tags ^^ Thanks for your help =) If I have more questions later on I'll post in the same thread. Oh by the way, are there any text editors that has ability to enter these symbols? I can't even find some of these symbols in the character map.

(Lol I just found that you could write symbols with the LaTeX feature) Oh I see. But if one of the symbols switched to the \exists (there exists one or more), then it would mean different things right? And here is what I have so far, the "iii)" is disproved:

Oh! I got it now thanks. But there's one more problem: In the "i)", it says "for all n, ..., which works for all m", and the rest are "for all m, ..., which works for all n"; notice that the n and m are switched. Wouldn't that affect the answer?

Assume n and m are natural numbers: Assume there exists a natural number j and natural number k: Assume: mn = (5j + 3)(5k + 4): = 25jk + 20j + 15k + 12 = 5(5jk + 4j + 3k) + 12 let i = 5jk + 4j + 3k mn = 5i + 12 Then mn does not equal 5i + 2 Then m = 5j + 3 and n =...