Number systems are at the heart of mathematics --- and have been for at least 4000 years. The Egyptians' had a base 10 system that used fractions, albeit not in the way we do, while the Sumerians remarkably developed a base 60 floating point system. What systems do we teach in schools? What about scientists, engineers and computer scientists these days? What about modern pure mathematics? The answers might surprise you.
Pure mathematics needs a bit of a serious shake-up. Sociologists ... please come to our rescue! Help us understand how we got into this mess, and what forces conspire to keep us in it.
In this video we explain how we (modern pure mathematicians) currently rely on a demonstrably fake arithmetic. Of course people will want to kick and scream at this claim, so we present some level-headed challenges that will clarify if my bold claim has merit or not. And we also connect with two important aims from classical calculus --finding the slope of a tangent, and finding the area under a curve. I assert that both of these important tasks can actually be done without infinite processes/limits -- and to find out how you can simply join the online Algebraic Calculus One courses (see below) currently for free. ;)
This video is in the Sociology and Pure Mathematics series, where we attempt to bring some human social/cultural analysis to modern mathematics: or at least outline some broad directions that such an investigation could take.
If you would like more discussion on the difficulties with "real numbers", check out my paper Set Theory: Should you believe? at https://www.researchgate.net/publication/280387313_Set_theory_Should_you_believe.
You can also look at the MathFoundations playlist found for example here courtesy of Cosmo Learning: https://cosmolearning.org/courses/math-foundations-with-norman-wildberger/video-lectures/
In particular look at the videos from about MF 84 to MF 123.
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/Norman_Wildberger
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/algebraic-calculus-one/
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 https://www.patreon.com/njwildberger
Your support would be much appreciated.