Real numbers and Cauchy sequences of rationals (II) | Real numbers and limits Math Foundations 112

Описание: There is a good reason why pure mathematicians cling so tenaciously to the idea of real numbers. They provide us with the ostensible `values' that lengths, areas, values of functions and solutions to equations seem to require. But is this all really just a dream??

In this video we have a new look at these notions, with a view of examining whether they really do support `real values', or whether perhaps they are intrinsically approximate notions. To motivate the discussion, we go back to a crucial calculation of Archimedes.

Video Content:
00:00 Introduction
3:08 Quantities determined approximately
5:08 Delusion of 'real numbers'
11:41 Definition of length, area, function value
17:15 Area
21:29 Function values
26:40 Solution of equations
31:42 Common aspect to kinds of measurements

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