Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82 скачать в хорошем качестве

Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82

We continue on with a short intro to interval arithmetic, noting the difference between the laws of arithmetic over the natural numbers and the integers. The case of rational number intervals is also briefly discussed. We end the lecture with some remarks on the vagueness of ``real number'' arithmetic. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. Video Content: 00:00 Intro to measurement and approximation 5:30 Multiplying intervals 9:10 An example of interval arithmetic 14:50 Laws of arithmetic for intervals with natural numbers 17:43 Arithmetic for intervals 21:52 Examples of interval multiplication 27:10 Laws of arithmetic for interval integers 29:33 Sub-Distributive law 31:49 Story with rational intervals 37:04 The serious problems with "real numbers" ************************ 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. *********************** 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 are being 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 Patreon,   / njwildberger   . Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист