Recent content by janac

@checkitagain i was not aware that you could do that (1/4 + 1/9 = <1/2). that was a nice a proof, but i can easily show that 1/x^2 is convergent by showing its integral is convergent. what i meant by post is that 1/x^2 tends to zero 1/x tends to zero 1/x^2 has a graph that...

@arildno That's a a pretty interesting concept. It makes sense that having an infinite number of terms does not suggests that the sum of these terms is also infinite. So in conclusion, we can says the harmonic series is not convergent because it does not approach zero fast enough. And our...

oops! I corrected that. That's a cool way of explaining divergence, (the bunch of terms add to one, but there's infinite bunches). But can't you say the same thing for 1/(x^2)? Yet 1/(x^2) is convergent

I understand that the harmonic series, \frac{1}{x} is divergent because: \int (1/x) from one to infinity is: [ln(infinity) - ln(1)] which is clearly divergent. BUT When I look at the graph of \frac{1}{x} versus \frac{1}{x^{2}} they both look like they are converging to zero as x...

I understand that a(b/c) = \sqrt[c]{}(a^b) so this suggests that (-1)(2/3) \sqrt[3]{}((-1)^2) = -1 right? Wolfram alpha and my calculator disagree.

Alright! I actually get it now! It is much easier to understand with variables and quantifiers, as opposed to english propositions. HallsofIvy, your example did break through to me quite well. This thread really motivated me to help other people on this forum. Much appreciation to...

Okay, so here are the facts I've picked out about implication. Please let me know if any of them are incorrect. p -> q -math has certain conventions to make life easier. Such as bedmas/pemdas, empty set, and the implication truth table -If the premise is false, the conclusion can be...

Okay, I understand that there are conventions in math, but I find it hardly likely that in a course like Discrete Math (which has a lot to do with proofs), that there would be an arbitrary convention based on the simple reason that its convenient. Okay fine, let us define a case which is false...

The truth table for implication looks like this p|q| p -> q ------------ T|T | T T|F | F F|T | T <----I'm trying to make sense of this one. My prof warned us that its strange. F|F | T I that implication means: "If p, then q" "q is necessary for p" "p is sufficient for q" "p, only...