Wednesday, June 02, 2021

FamousMathProbs: the relation between fractions and other number systems (English)

See also:
How to set up fractions
We give an overview of number systems generally, with an idea of positioning the rational numbers and their relation with other systems, like natural numbers, or integers or complex numbers etc. But crucially the usual "real numbers" are really a fantasy that ought not to be part of your understanding of abstract number systems in pure mathematics.

As the ancient Greeks realized, the natural distinction between counting and measuring leads us to different kinds of number systems. While counting naturally involves natural numbers and extensions of them, measuring leads to more geometrical numbers, for example line segments.

This lecture is certainly at odds with the majority opinion these days about "numbers". High school teachers and undergraduates can benefit by thinking about these important issues.

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