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Read this : Negative numbers, by A. N. Whitehead

Alfred North Whitehead, professor of mathematics and philosophy, and famous for his collaboration with Bertrand Russell on their joint effort, the Principia Mathematica, also wrote a book, “Introduction to Mathematics”, in 1911, for High School students and others who really wanted to know what math was all about.
The section on negative numbers is so relevant to the teaching of that topic today that it is a MUST READ. Click the link to download this section.

Alfred North Whitehead: Introduction to Mathematics

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