Recent content by dgambh

I agree with fresh. I'll add functions and families of sets to the list of things you need to know. George Simmons book, for example has a first chapter reviewing a lot about sets. I think other books do the same. Also, take a look at this. I think this link is legal since is from steklov...

I would suggest to get learn a bit of set theory and how to proof things about sets, some topology textbooks have an introduction chapter about this, but usually is very brief. Also, it depends on the person. But I have found reading some popular textbooks to understand what topology is about...

Maybe you'll like Concepts of Modern Mathematics by Ian Stewart. And I would recommend any John Stillwell book. I loved his book on set theory and real numbers. He has a cool book on algebra, and another on number theory and geometry. Right now I'm reading his book on surfaces. Also, I look...

L'Hopital's rule says ##\lim_{x -> a} \frac{f(x)}{g(x)} = \lim_{x -> a} \frac{f'(x)}{g'(x)}## if both ##f(x)## and ##g(x)## tend either to ##0## or ##\infty## as ##x -> a##. Maybe you're using the quotient rule for derivatives which is wrong, because that's not what the rule says.

Remember ##0 < x < 1##. Also you don't need to think this in terms of derivatives.

I've been watching The Mechanical Universe lately, and have found it really good. Maybe this episode will interest you. It has a lot of historical context that explains where the first law of Newton comes from.

I am not sure if this helps but what if you multiply by the conjugate and then try to think why ##\lim_{y \to \infty} \left(1 - \frac{1}{y^2}\right)^y## should be 1.

Hello, everyone. I've been following these forums occasionally for about 2 years now, and I kind of like the community and share some of the interests of people on these forums. So I'm from Colombia (South America). I am in my mid-20s and I am an undergrad in mathematics in Colombia. I used to...