Recent content by Slats18

For (i), your topology T is the set of all open sets A x B such that A is an element of T_x, and B is an element of T_y. X is an element of T_x, as it is required to be one by the same rules we a re trying to prove, as well as the empty set, and vice versa for Y being an element on T_y. Use this...

You're doing great at the moment, there's just a few more steps to the proof. Consider two cases: a,b are even, and a,b are odd. a,b being even is very similar to the irrationality proof of sqrt(2), just as jedishrfu said. So, now consider when they are odd, and substitute simple expressions for...

First of all, you should know that standard deviation is independent of translation (change of origin), but is affected by scale. See if you can knock out the proofs of each separately, and then you should be able to put them together. Also, begin your proofs by using the variance, not the...

Should be 4-isopropyl-2,5-octadiene, I believe.

IMO, you should always show your working, so you should add how you simplified your numerator, as it's not entirely obvious by inspection =)

Try "Real and Complex Analysis" by W.Rudin.

There is a few more you could write down. For instance, there are 3000 young people, and you know that 1320 of them are young males. Can you make a statement about how many young females there are, and then use this method to find other amounts?

Gotta agree with Manu Mop here. Given integer ab, where a,b are part of the counting integers 0 to 9, the next number is ab-((a-b)*b) 73-((7-3)*3)=61 61-((6-1)*1)=56 56-((5-6)*6)=62 62-((6-2)*2)=54 Bit obscure, but it fits...

Ohh, duh, of course haha. My mistake, I'm doing topology and complex analysis so sometimes the two subjects mix haha.

Could it be also said, not neccessarily proven, that because the mapping is from R to R, the pre-image is not defined for certain R and hence, not continuous? Ex: Take the interval [-1,0). The preimage of this is obviously in the complex plane, hence not in R.

On further, concentrated inspection, given [x,x+r) the pre-image of this is ( -(sqrt(x+r)),-(sqrt(x)) ]U[ sqrt(x),sqrt(x+r) ) which isn't open as -sqrt(x) is an element of the pre-image, but there is no r > 0 such that [-sqrt(x),r) is an element of the pre-image as well.

Sorry for the really late reply, been busy with other topological concerns, namely product topologies haha. I'm completely blanking on this at the moment, no matter how interesting topology is, it just doesn't stick. Would it be [sqrt(x),sqrt(x) + r) ?

Think of it as a transformation. You've got some ball C, centered at (0.5,0.5) with a radius of 2. Now, C+(0.5,2.5) is the set of all points in C, in addition with the point (0.5,2.5). So, where in R^2 are these points now?

It was only by inspection, assuming that any sets in the negative real line for this particular function don't have pre-images in the real line. If that assumption is wrong, then I've got nothing to go on to prove it's not continuous, so it must be, but that's a very weak justification.

Is the function f: R -> R, x -> x^2 continuous when the domain and codomain are given the Half interval topology? (Or Lower Limit topology). I'm not sure where to go with this. On inspection, I know that the intervals are open sets, so preservance of open sets in preimages are defined for x >...