Recent content by vadik

I'm lost! My book of topology says that its possible to construct a (continuous!) function f:[0,1] -> R^n such that the image is a ball {x: |x|<=1} I can't imagine how is it any possible to do such things. The book doesn't give any example or prove of it. It's just a comment. Any ideas? I...

Construate the function of profit(price of a car), what means find out how does the profit depend on the price. Then find the maximum of that function using derivatives.

Thank you. :) integral (cos x)^2 dx

Do anyone have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!

is there any other set, whiches cardinality is zero exept the empty set? I don't think so

isn't it a null set? or an empy set?

ok..maybe my english is not good enough.. what is that called: ø?

well, sin(x/2) is already a periodical function with period pi, so even if you construct a furier series of this one you would get the same: sin(x/2)

It exists to make difference between "something" and "nothing". A set that contains something is like something and the null set is nothing (contains nothing)

if I understand right "a vector at a point" means that we take the point and let the vector start from it. So if a vector 2i + 3j starts from point (1,2), thet its endpoint will be at (1+2,2+3)=(3,5).I made a picture, so you will understand what i mean. When you write a vector in polar...

r means the distance from origin to the end point of the vector. Theta is the angle between x-axis ant the straight line from (0,0) to the end point. So, when you have a notation in polar coordinates (r, theta) you can convert it to cartesian calculating x=rcos(theta) and y=rsin(theta). But when...

What I meant is like, when you see a definition of a derivative [f(x+h)-f(x)]/h, you don't just remember by heart "ef ex plus eich minus ef ex divided by h" and say "I know what derivative is", but you try to understand what the equation contains and finally understand that it means the velocity...

It is up to yourself will you understand things deeper or not. When there's a definition or a theorem in a book you might just agree with it or think for a while to understand what does it really mean.

I learned a lot of vectors in Stanley I. Grossman's book "Multivariable calculus, Linear algebra and Differential equations" Though the book might be expensive.

Power set of C includes all subsets of C, which means that it also includes all subsets of a subset (B). Thus it includes the power set of B. Is this formal enough?