Recent content by rebeka

OK thank you! I think \neg \exists x \exists y (x \in y \wedge y \in x) puts the whole of the picture into perspective for me. I still don't understand your first reply because if \phi(x) = x \in x is the chosen equation where is the y in the equation that cannot be free? I had been...

I guess I am expecting that what it should be saying is if x \in y \implies y \not\in x but I don't get this from your answer. Your answer is suggesting that if x \in x \implies Russels \; Paradox [edit] sorry I guess that holds too if I do it as you seem to have .. take x \in y then...

I am still having a hard time with this and it is a problem I am having in general. I don't understand how to take the first steps. The ones that follow are very obvious to me but when I have to ask myself well what makes this work I get stuck! And I am still a little unsure of my decision to...

Yeah, no I get that, it's this definition that is giving me trouble. I think where I went wrong was I forgot to assume that x is a member of y and as a result of Russells Paradox and the negation of the Axiom of Comprehension well, the rest follows. I'm taking this from Basic Set Theory by...

\exists x \phi(x) \implies \exists x ( \phi(x) \land (\forall y \in x) \lnot \phi(y)), where \; y \; is \; not \; free \; in \; \phi(x) I understand what Russels Paradox is saying and what the difference is between a subset and a member but I'm having trouble with this definition of...

With respect to iii) it was an example where I am becoming confused with respect to the usage of brackets and what they signify. Different brackets seem to have different meanings at different times. In this case the square brackets are addressing the class A where the definition in the text...

I'm reading the book Basic Set Theory by: Azriel Levy as I thought it might help me better understand Group Theory and Matrix Math. I have read the first chapter a number of times but I keep getting hung up on some of the syntax of the basic language or language of first-order predicate...

Thank you both! o~o

Homework Statement L = \frac{a}{\sin{\theta}} + \frac{b}{\cos{\theta}} find L in terms of a and b where L is a maximum ... Homework Equations place long list of trigonometric identities here??The Attempt at a Solution so my attempt looks something like this: as a cause of the chain rule...

That's awesome ... I wish I had come up with this myself with all the time I spent trying to figure it out ... but I'm glad to get it out of my head, it's been stuck there for a while. Thanks again!

Thank you for redirecting my approach!

Five years ago I posted this question. At the time it was difficult for me to understand almost all of what I was trying to learn and was very frustrated. I put it down and studied other stuff including math. I just looked at this question again and am finding myself still unable to derive...

'tis true... o-o

I mean just for starters \frac{2}{r+2w} = \frac{1}{w} looks to be \frac{1}{|\vec{U}|} and \frac{1}{\sqrt{(x_0-x_1)^2 - (y_0-y_1)^2}} looks to be \frac{1}{|\vec{V}|} except that there's a negative in there? A few thoughts on that, inverted y screen coordinate <= probably not -.- ok one...

From this example Anti-Aliasing section 22.4.1 http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter22.html what does the following equation represent and how was it derived? k = \frac{2}{(2r+w)\sqrt{(x_0 - x_1)^2 - (y_0 - y_1)^2}} I assume the 4 sets of linear equation...