Recent content by titaniumx3

Now I'm getting confused lol. According to the definition of NG(H) from my original post, we want to show that for all g in NG(H), g-1 is also in NG(H). In other words we have to show that for any g in NG(H) and all x in H, (g-1)-1x(g-1) is H. Am I correct in saying this?

It tells me the inverse of g-1xg is g-1x-1g (which must also be contained in H), but how does that show that g-1 is in NG(H)? (i.e. do all elements of NG(H) have inverses?).

It's the identity. But, aren't we supposed to show that (g-1)-1x(g-1) = gxg-1 is in H?

Let G be a group and H a subgroup of G. We define the following: N_{G}(H) = \{g \in G \,\,|\,\, g^{-1}hg \in H,\, for\, all\,\, h\in H\} Show that N_{G}(H) is a subgroup of G. _______________________ I've shown that for all x,\, y of N_{G}(H), xy is an element of N_{G}(H), but how do...

Anyone? :)

Isn't 1+1=2 taken as an axiom (of sorts) hence it requires no proof. I don't understand why this needs to be proved for.

Homework Statement Prove that every triangle-free graph G on n vertices has chromatic number at most 2\sqrt{n}+1. Homework Equations The chromatic number of a graph G is the smallest number of colors needed to color the vertices of a graph so that no two adjacent vertices share the same...

Are there geometries where such an object could be constructed or is that a silly question to ask?

May I ask, when someone discusses "limiting processes", what exactly does that mean? Does it simply refer to things like the sum of an infinite series, calculation of differentials/integrals? What about taking the limit of a function or sequence, is that also a limiting process? BTW, I'd like...

Yeah, Islamic mathematics definitely came after the Greeks, lol but in any case it would be interesting to know if they used any similar methods. I do recall reading somewhere about exhaustion methods being used by the Chinese but I've lost the link and can't verify it.

Can anyone give some historical examples of methods of exhaustion being used to solve problems. One popular example is the method Archimedes used to find the lower and upper bounds of the area of a circle (and therefore Pi) by inscribing circles inside and outside a circle? In particular I'm...

I'm not entirely sure how you'd show it rigourously and in all honesty I'm not sure if it makes any sense at all with regards to L_1 but, 1 = sqrt(1) = sqrt(sqrt(1)) = sqrt(sqrt(sqrt(1))) = ... That said, the above is using only the representation of L_1 in my previous post, not in the a_1 =...

Hmmm, I think I'm probably getting myself confused lol. Say the two equations I posted have limits as k tends to infinity, L_{1} and L_{2} respectively and we consider the case where n = 0. Then, L_{1} = \sqrt{0+\sqrt{0+\sqrt{0+...}}} = \sqrt{\sqrt{\sqrt{...}}} and, L_{2} =...

Well, in the first (original) limit, for n=0 say, it's not clear what value is contained in the first square root, where as in the second limit I posted, it is clear that the value contained in the first square root is 0; hence the limit would definitely be 0.

Looking at the above, given the definition of a_{1} and a_{k+1}, we are told, \lim_{k\to\infty}a_{k} = \sqrt{n+\sqrt{n+\sqrt{n+...}}} But, this to me seems to be either false or slightly misleading. Shouldn't it actually be, \lim_{k\to\infty}a_{k} = ...\sqrt{n+\sqrt{n+\sqrt{n}}} Are...