In this video we ask the question: how do standard treatments of calculus and analysis deal with the vexatious issue of defining real numbers and their supposed arithmetic??

We pull out a selection of popular Calculus and Analysis texts, and go through them with a view of finding out: what exactly is a real number? All the books I examine are excellent booksaside from their treatment of foundational issues, where we see that they mostly fall clearly short.

We look at Calculus texts by Steward, Sallas Hille and Etgen, Rogawski, Courant, Spivak, Caunt, Apostol, Keisler and Adams, and Analysis texts by Spiegel, Apostol, Royden, Kolmogorov and Fomin, and Rudin.

This video really should be an eye opener to students of mathematics. Yes, it is possible to challenge the standard thinking, and the mathematical world need not collapse. Admitting current weaknesses, and the lack of acknowledgement of them by the Academy, is an important step in moving forward to a newer, better mathematics.

Video Content:
00:00 Intro to flaws in modern treatments of "real numbers"
3:28 Text books that tackle real numbers
21:28 More text books
35:54 Advanced text books

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

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