Real Analysis Exam 2 Review Problems and Solutions

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@kisungyou6505 Жыл бұрын

As a junior faculty member, I admire how you ask students to have time of consideration between what definitions refer to. We often forget definitions are defined for reason.

@billkinneymath Жыл бұрын

They are very important!

@gabrielleonard6743 5 ай бұрын

I really appreciate your efforts Mr Bill, these videos are helping us at the university of Namibia.

@billkinneymath 5 ай бұрын

Awesome to hear! Let me know how you do in your course!

@vincentzevecke4578 3 ай бұрын

Bill, you help me to understand by norm and Riemann

@vincentzevecke4578 3 ай бұрын

You have greatly help me to understand Hilbert spaces, thanks

@afoster1955 Жыл бұрын

Hello Bill, I love the content. Your explanations are second to none. I can't wait for you to explain "Compactness". I have one question: In these epsilon/delta definitions of limit and continuity of a function (at a specified point of a set U or I), shouldn't the existing delta be dependent upon the given epsilon? I want to thank you for your content.

@billkinneymath Жыл бұрын

Thanks! Yes, the delta is dependent on the given epsilon. Sometimes that is emphasized with function notation δ(ε) but sometimes it's just understood.

@afoster1955 Жыл бұрын

Hello again Bill. Since you're covering "Baby Rubin" so thoroughly. Is it possible for you to provide some (possibly detail) explanation as to how Rubin comes up with the number "p + 2" in showing that a certain set of real number have "gaps". If memory serves me, this is located in the very beginning pages of Principles of Mathematical Analysis 3rd Edition. I think this would be helpful to me and to others. Thanks in advance Bill

@billkinneymath Жыл бұрын

Actually, I have an article about that exact topic. Here it is: infinityisreallybig.com/2021/01/07/baby-rudin-let-me-help-you-understand-it/

@oof_marcieee 2 жыл бұрын

You're the most amazing person ever!!!

@billkinneymath 2 жыл бұрын

Glad it was helpful for you!

@isaaccastro7853 Жыл бұрын

On question 12 does the constant function f(x) = c for some constant real number work as a counter-example?

@billkinneymath Жыл бұрын

If you allow monotone increasing to include constant functions in your definition of monotone increasing, then it does. If you don't, then it doesn't (sometimes people call it "strictly" increasing for the second case).