Recent content by josueortega

I understand the part of the conjugate, actually the whole part on the left is pretty clear to me. The problem is the right side of the inequality. I don't understand how $$\sum x_i^2 \sum y_i^2 = \sum_{j=1}^{n} |x|^2 \sum_{j=1}^{n} |y|^2$$

Hi everyone, I am working on my own through Rudin's Principles of Mathematical Analysis and, after the demonstration of Cauchy - Schwarz Inequality, in Theorem 1.37, part (d), Rudin states: $$|x \cdot y| \leqslant |x||y|$$ When he explains how to prove this, he simply states that this...

I think I got it now! We know that $$|Re(x)| \leqslant |x|$$ $$ [Re(x)Re(x)]^{1/2} \leqslant |x|$$ $$ Re(x) \leqslant |x| $$ which is what we wanted to prove. Right?

Hi everyone, I have a question on Rudin's proof of Theorem 1.33 part e. Here he prove the following statement: The absolute value of z+w is equal or smaller than the absolute value of z plus the absolute value of w -Yes, is the triangle inequality, where z and w are both complex numbers-...

Thank you.

Thanks. I am trying to get it now. But the fraction I wrote above is h, NOT x.

Don't get it. How can it be not less than 1, and at the same time, less than one? I think the more likely answers are that: 1) No need to prove the existence of h 2) There is something I'm missing about y=sup E, where E is the set all positive real numbers t, such that t^n<x By the way...

Hi! I need some help here, please. In Principles of Mathematical Analysis, Rudin prove the uniqueness of the n-root on the real numbers. For doing so, he prove that both $y^n < 0$ and that $y^n > 0$ lead to a contradiction. In the first part of the proof, he chooses a value $h$ such...