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 divisbyzero.com
Cardinality of infinite sets, part 1: four nonstandard proofs of countability - David Richeson: Division by Zero
| | thatsmaths.com
Parity and Partition of the Rational Numbers. Part II: Density of the Three Parity Classes - ThatsMaths
2.4 parsecs away

Travel
| | In last week's post, we defined an extension of parity from the integers to the rational numbers. Three parity classes were found --- even, odd and none. This week, we show that, with an appropriate ordering or enumeration of the rationals, the three classes are not only equinumerate (having the same cardinality) but of equal...
| | jaydaigle.net
A Fictional History of Numbers, Part 4: Imagination, Complexity, and the Fundamental Theorem of Algebra
3.7 parsecs away

Travel
| | We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating.
| | theoremoftheweek.wordpress.com
Theorem 18: the rational numbers are countable | Theorem of the week
2.9 parsecs away

Travel
| | One of the intriguing facts about infinity mentioned in that Horizon programme (the one on recently thatI disliked) is that there are different sizes of infinity. I thought that this week I'd start discussing that fact. (There might be another theorem of the week on this subject!) Here are two questions for you to consider....
| | ropmann.wordpress.com
Clover | Roland's Photo Blog
16.6 parsecs away

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