Alright, this is what I've got for part 2)
If I let abv(x-y)<\frac{a}{N}, then I can say that abv(Nx-Ny)<a, meaning abv(Nx-Ny)\in[-a,a].
Now if I let abv(F(x)-F(y))<\frac{m}{N}, I can say that abv(NF(x)-NF(y))<m because of part one of the proof. Since \frac{m}{N}<\epsilon, I can then say...
Also when I say subk, I mean subscript k. The subscript formating on here doesn't seem to work right for me. I am trying to show that I had added f(x) to itself k times
in mathematical induction the objective is to prove that n=k being true implies that n=k+1 is true. if you can show this, the statement is considered true. at least that's what we were taught. BTW this is weak mathematical induction.
Now I've figured out something with part 2. If m/N is less...
Ok this is a proof I'm having trouble with. I've given the solution for the first part I got but I'm stuck and I'm not sure if the first part it correct. any help is appreciated
Homework Statement The purpose of this project is to ascertain under what conditions an additive function has a...
1. show that for each positive integer n and each real number x, f(nx)=nf(x).
Homework Equations
f(x) is an additive function (f(x+y)=f(x)+f(x))
The Attempt at a Solution
Well I'm thinking that I can just use mathematical induction to show that:
1) f((1)x)=1f(x)...
Im currently taking an introduction to real analysis class and here's the problem. I do very well with all the math I've encountered before this. I'm really not doing well with the abstract nature of real analysis. I'm having trouble proving things in general because of the fact that i have...
Define the sequence A where Asub1=a and Asubn=sqrt(a+Asub(n-1)) for n greater than or equal to 2
I need to determine what positive choices of a will make the sequence converge and to what limit. I also need to prove it.
I plugged some values into the sequence and found that it seems to...