Math Foundations/B/110

117. The continuum, Zeno's paradox and the price we pay for coordinates
xYPw2gY_3PI What is space? Time? What appears to be smooth, uniform, and divisible, turns into an illusion.

Model the Continuum
Zeno's Paradox
 * Famous Math Problems/A #19

Another Version of Zeno's Paradox
You can't do an infinite number of things

The price we pay for coordinates
The geometry of the Cartesian approach does not automatically obey all our Euclidean/physical assumptions!

119. Mathematics without real numbers
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1

 * If we faced the (logical) music, and accepted the current weaknesses with real numbers, what would happen to mathematics??
 * Until recently, most mathematicians would have assumed that analysis, differential geometry, large parts of topology and algebraic geometry would largely collapse!!
 * It turns out that this is not the case: all these subjects would in fact be revitalized!
 * But serious work is required!

This list continues on Math Foundations/B/120, etc.