# Josué Molina

less info
reputation
624
bio website molinajosue.blogspot.com location Houston, TX age 24 member for 2 years seen Feb 28 at 17:27 profile views 307

One Thousand Birds

# 445 Actions

 Mar12 revised Uniform Convergence of a Nonlinear Sequence of Functions #1 I made the title more accurate for future searches. Mar12 comment Uniform Convergence of a Nonlinear Sequence of Functions #1 Never mind. I wrote out the terms of the sums and saw why we did that. Thank you very much, guys! Mar12 answered Can I prove (if $n^2$ is even then $n$ is even) directly? Mar12 accepted Uniform Convergence of a Nonlinear Sequence of Functions #1 Mar12 comment Uniform Convergence of a Nonlinear Sequence of Functions #1 I agree. My apologies. I immediately saw it when I remembered the exponent laws. I have another question: In the second step, I know that we start the summation at $1$ and not $0$ because the summation term at $0$ cancels out with the $n$. Similarly, in the third step, we can start the summation at $2$ and not $1$ because the summation term at $1$ cancels out with the $\ln x$. In the fourth step, I know that we change the index of the summation to revert back to the definition. However, I do not understand how we reached the fifth step. Did we use partial fraction decomposition? Mar12 comment Uniform Convergence of a Nonlinear Sequence of Functions #1 Could you clarify to me how $\sqrt[n]{x}=\exp\left(\frac{\ln x}{n}\right)$? Mar12 revised Uniform Convergence of a Nonlinear Sequence of Functions #1 I added an edit. Mar12 asked Uniform Convergence of a Nonlinear Sequence of Functions #1 Mar12 comment Pointwise Convergence of a Nonlinear Sequence of Functions Thank you! But I did not understand one thing: Why do we have to separate it into two cases, where $x\neq1$ and $x=1$? EDIT: Never mind, I saw it: It is because the limit is $0$. Mar12 accepted Pointwise Convergence of a Nonlinear Sequence of Functions Mar12 revised Pointwise Convergence of a Nonlinear Sequence of Functions I added an edit and changed a bit of the LaTeX. Mar12 revised Pointwise Convergence of a Nonlinear Sequence of Functions I changed the title. Mar12 accepted Applying Euler's Theorem to Prove a Simple Congruence Mar12 asked Pointwise Convergence of a Nonlinear Sequence of Functions Mar8 accepted What is the meaning of the double absolute value bars in this context? Mar8 asked What is the meaning of the double absolute value bars in this context? Mar7 accepted Uniform Continuity of a Sequence of Functions with a Piece-Wise Defined Limit Mar7 comment Uniform Continuity of a Sequence of Functions with a Piece-Wise Defined Limit This is what I now have: Over the set $(1,\infty)$, we see that $|h_n(x)-h(x)|=|x/(1+x^n)-0|=x/(1+x^n)<1/2$. Is this sufficient to show that the function converges uniformly over that interval? Mar7 comment Uniform Continuity of a Sequence of Functions with a Piece-Wise Defined Limit I just needed to find a set over which the sequence converges uniformly. :) I will try the set $(1, \infty)$, as you suggested. Mar7 comment Uniform Continuity of a Sequence of Functions with a Piece-Wise Defined Limit But could it be shown that it is uniformly continuous over a smaller set?