Recent content by gilabert1985

Hi, I have this problem that is solved, but I don't understand the theory behind it. It says: Which of the following sets, with the natural definitions of addition and scalar multiplication, form real vector spaces? A) The set of all differentiable functions f:(0,1)\rightarrow\Re such that...

However, they would not hold for negative values of n? I am confused :/

Thanks! So that would give me 2/(n^3+4)>1/(n^3+4), which holds when n goes to infinity. So could I use something similar for part C then, something like b_n=0 or b_n=1? With b_n=1, I could have a_n=(2n^3+1)/(2n^3+1)?

Hi, I have the following problem and have done the first two questions, but I don't know how to solve the last two. Thanks for any help you can give me! Homework Statement Let a_{n}\rightarrow a, b_{n}\rightarrow b be convergent sequences in \Re. Prove, or give a counterexample to, the...

Hi everyone! I have the following problem which I don't understand... It is already solved, but there are three questions I have regarding it. The problem says: "Let S be the set of all vectors x=(x_{1}, x_{2}) in \Re^{2} such that x_{1}=1. What is the span of S?" And here is the answer...

Hi, I have the following problem that is part of a project, and I have been stuck on it for the last couple of hours ... Thanks a lot for any help you can give me! It says: "An affine mapping from V to W, where W is a second real vector space, is a mapping f:V\rightarrowW such that for all...

Hi, I have to solve this problem... I have done something, but I don't know if it is right :/ Thanks a lot for your help! "Show by induction that (1-nu)(1+u)<=1 for n=0,1,2,3... and u>-1" For n=0: (1-0*u)(1+u)^0 <=1 1*1<=1 1<=1, which is true. Assume that the statement is true for...