May14 awarded Caucus Mar27 awarded Informed Mar18 awarded Scholar Mar18 comment Why is $f:\mathbb{R} \to S^1, f(t)=(2\pi \cos(t), 2\pi \sin(t))$ not closed?Couple of minutes after I have posted the question a friend of mine gave me a solution, which made me think exactly this solution. thanks :) Mar18 accepted Why is $f:\mathbb{R} \to S^1, f(t)=(2\pi \cos(t), 2\pi \sin(t))$ not closed? Mar18 asked Why is $f:\mathbb{R} \to S^1, f(t)=(2\pi \cos(t), 2\pi \sin(t))$ not closed? Jan11 awarded Announcer May16 awarded Yearling Mar10 awarded Critic Mar9 comment Are there any calculus/complex numbers/etc proofs of the pythagorean theorem?I learned linear algebra this semester, and yes, this proof is really cool! Sep18 awarded Nice Question Sep18 awarded Commentator Sep18 comment Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$I see, well it gives us information actually. From the symmetry of $1_\mathbb{Q}$, it doesn't matter which value does the function get around $x=0$ the change in the function is zero, just like the limit says. Sep18 comment Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$I don't understand what you wrote, what does $1_\mathbb{Q}$ mean? Sep18 awarded Editor Sep18 comment Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$I have modified my question, I know that when the derivative exists this limit is equal to it, but can it be used when the derivative is not defined? Sep18 comment Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$I know, I have modified my question to clarify this issue. Sep18 revised Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$added more information Sep18 asked Uses of $\lim \limits_{h\to 0} \frac{f(x+h)-f(x-h)}{2h}$ Sep11 awarded Autobiographer