Thank you. Let me see if I understand this right,
As before with X = {1,2,3,...} and
if A_{i} = 2i and A_{j} = 2j-1, then A = \bigcup_{i}^{\infty}A_{i} = 2,4,6,... and A_{\infty}^c = \bigcup_{j}^{\infty}A_{j} = 1,3,5,...
If A^c is defined to be finite, we have A_{n}^c =...
I am trying to better my understanding of \sigma-algebras, and I have a bit of an issue with one of the examples. This is from Cohn Measure Theory, and before I give the problem, here are two definitions:
Let X be an arbitrary set. A collection \delta\Large of subsets of X is an algebra on X...
I have used your advice and went about it in the following way:
For a small slice of thickness \Delta{x} a small change in energy will be given by
de = c(x,u)du
Dividing by du I obtain e_{u} = c(x,u).
From the Fundamental Theorem of Calculus, this really says that
e(x,t) =...
Homework Statement
Show that the heat energy per unit mass necessary to raise the temperature of a thin slice of thickness \Deltax from 0^o{} to u(x,t) is not c(x)u(x,t). but instead \int_0^uc(x,\overline{u})d\overline{u}.
Homework Equations
According to the text, the relationship...
Hi, I am in need of some expert advice please.
I am enrolling for my honours degree in mathematics next year. I am trying to mix it up in order to have a strong foundation in pure mathematics with specialisation in applied mathematics. My interests are financial mathematics, probability...