Recent content by ANphysics

But aren't you assuming here that distance is defined to be the absolute value of the difference between two elements. Is this true in general for any metric space? For example, we can consider the vector space of all functions defined on [0,1] and define an inner product to be < f(x), g(x)>...

Lets say that we have two Cauchy sequences {fi} and {gi} such that the sequence {fi} converges to a limit F and the sequence {gi} converges to a limit G. Then it can easily be shown that the sequence defined by { d(fi, gi) } is also Cauchy. But is it true that this sequence, { d(fi, gi) }...

I completely overlooked the absolute value sign. Thank you for pointing this out!

Dirichlet's Approximation Theorem not working for n=8 and α= pi? I am reading a number theory textbook that states Dirichlet's Approximation Theorem as follows: If α is a real number and n is a positive integer, then there exists integers a and b with 1≤ a ≤ n such that |aα-b|< 1/n . There...

I believe that something that could be useful here is the fact that voltage is the same across all elements that are parallel to one another in a circuit. I'm just not sure what you mean by the total current running through the series is 4 amps. Do you mean that the total current running through...

I am study chapter 5 of An Introduction to Thermal Physics by Schroeder and I am having trouble understanding his explanation of the differences between enthaply, Helmholtz free energy, and Gibbs free energy. Schroeder defines enthalpy of a system as its energy plus the work needed to make...