Category Archives: Mathematics

Mathematical Inventions

A friend of mine recently commented, in The Secrets of Pi, a post on this blog, that pi, like the circle, like plane geometry, and like all math, are, of course, and obviously, inventions made up by mathematicians. This is … Continue reading

Posted in Mathematics, Philosophy | Tagged , | 5 Comments

Cardinality of the Natural Numbers

Cardinality of sets is a basic concept of set theory, but Georg Cantor extended the range of the idea when he applied it to infinite sets. Cardinality, simply explained, is just the count of elements in a set. The cardinality … Continue reading

Posted in #philosophical, Mathematics | Tagged | 17 Comments

The Secrets of Pi: 3

Arcus reminded me that the debate we had about pi concerned the cardinality of the decimal number expansion. There are an infinite number of digits, but is this a countable infinity, or is it of the same order as the … Continue reading

Posted in Mathematics | Tagged | 11 Comments

The Secrets of Pi: 2

It has been mentioned that the depths of Pi contain not only amazing texts, such as every draft Einstein wrote of his theories and threw away, but even images such as TV images from Hitler’s opening speech of the 1934 … Continue reading

Posted in Mathematics | Tagged | 4 Comments