Recent content by mariush

Exactly! Thanks a lot :)

Hi! Given a function r:\mathbb{R} \rightarrow \mathbb{R}^2, r(t) = (f_1(t), f_2(t)), is there a way to analytically determine if there are points (x1, x2) where r(t) = (x1, x2) for multiple t-values? Lets say i was to find such points for the function r(t) = (t^3-t, 3t^2 + 1) How...

First thought. 5 is a simple integrer. e is calculated as a limit or by series expansion.

Homework Statement f:R->R is defined as f(x) when x\neq 0, and 1 when x=0. Find f'(0). Homework Equations The Attempt at a Solution Since I can prove that f is continuous at x=0, does that allow me to take the the limit of f'(x) as x-> 0, which is 0? It is quite easy to...

Yes! I agree guys. Thanks a lot for the help and patience :)

Ok. But |x-y| is one metric. The general case d(x,y) could be anything as long as it follows the four conditions of a metric.

Sorry. It was a minus sign in my head. I'll edit it.

Hi, thanks for all the good help! I've been thinking about what you said, and I still feel a bit unsure. When x_n is a sequence, x is a limit if d(x_n, x)<\epsilon when n>N, by definition. So let's say that d is defined as 2|x-y|. If we let z_n=d(x_n, y_n) where z_n, x_n, y_n are...

Great! Could a solution to the problem be something along these lines?: Since x_n \rightarrow x , y_n \rightarrow y, we know that d(x_n, x)<\epsilon, d(y_n, y)<\epsilon for any n>N. And since x_n, y_n lay within an \epsilon interval from x, y for n>N, -2\epsilon +d(x,y) <d(x_n, y_n)<...

Thanks once again! I was wondering about just that: d(x_n,y_n), d(x,y) =|d(x_{n},y_{n})-d(x,y)| Are you certain about this? It would definitely make it simpler, but is not |A-B| the definet metric in the eucledian plane? Edit: If we allow limits, i agree that once we know that...

Thanks. I think i almost could show it. Since x_n, y_n converge, there is a N so that d(x_n, x) <\epsilon and d(y_n, y)<\epsilon for n>N. (We pick the largest N of the two) Now, since x_n, y_n lay within less than \epsilon distance to x, y, -2\epsilon + x + y < x_n +y_n < x+y+...

Homework Statement Let \left (X,d \right) be a metric space, and let \left\{ x_n \right\} and \left\{ y_n \right\} be sequences that converge to x and y. Let \left\{ z_n \right\} be a secuence defined as z_n = d(x_n, y_n). Show that \left\{ z_n \right\} is convergent with the limit d(x,y)...

Does not the time of day question rely (for any practical aspect) on in what intervals we count time?

Definitely a good question. As far as i recall, time is not quantized in the SM, but the gap between 23:59.99 and 00:00.01 would at least be quite huge

But is time not continuous?