Recent content by bhagwad

YES, that is excellent! Thank you!

Right ho. Thanks!

This explanation seems fine if you say that the electron feels the field after one year. I guess my question would be "How does the circuit know that it's been completed?"

I'm familiar with the macro way of looking at it already. Just like I studied thermodynamics in college and know about the general behavior of such systems, I also like to know what it is that an individual particle is "feeling". Basically I want to know what happens if I'm an electron and the...

These are very "macro" answers. While I know about potential differences and electric fields, but I'm not certain as to the exact force felt. Does the electric field travel as fast as the speed of light? How does the electron on Earth even know about what's happening on the moon? What if the...

Say I have a copper wire connecting the Earth and the moon (or some other large distance). The Earth side is touching a "negative" source and the moon is about to touch a positive one". As soon as the connection is made, how do the electrons at the Earth know about it? Obviously the signal can't...

Thank you very much! I actually drew the lines on the paper and am trying to figure it out. Excellent explanation!

In definition 2.17 of Rudin's text, he says that a set E is convex if for any two points x and y belonging to E, (1−t)x+ty belongs to E when 0<t<1. I learned that this means the point is between x and y. But I'm not able to see this intuitively. Can anyone help me "see" this?

Based on the state of science so far, I'm of the opinion that free will does not exist. When I say "free will", I mean that our thought processes and bodies are controlled entirely by natural laws. If our brain is governed by classical principles, then it's completely deterministic. If there are...

Thank you very much! I've been reading up Landau myself now.

I linked to your reply from my blog post: http://www.bhagwad.com/blog/2013/uncategorized/missing-steps-in-theorem-1-21-of-rudins-principles-of-mathematical-analysis.html/ Thanks again!

My question is why didn't Rudin simply define t as t=y-k instead of t\ge y-k?

Thanks that works! It's curious though. We've proved it in one direction, but I wonder how someone made the formula in the first place.

So if we have b^3-a^3, we get (b.b.b)-(a.a.a) I'm probably missing something obvious, but I'm not sure what to do from here on.

Rudin Theorem 1.21. How does he get "The identity"? In Theorem 1.21, Rudin says: The identity b^n-a^n=(b-a)(b^{n-1}+b^{n-2}a+...+a^{n-1}) yields etc etc. What is this "identity", and do we need to prove it first? If not, what assumption is Rudin making?