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# Tag Archives: Peano arithmetic

## Infinity and Foundation

After the reviving effect of a week’s holiday, I have been thinking about Zermelo–Fraenkel set theory, inspired by a very nice student project I supervised (about which I hope to say something here sometime soonish). I have come across a … Continue reading

## On foundations

Jack Edmonds stayed in my house for two and a half weeks, while giving his two courses on polyhedral combinatorics in London (I reported on the second one here). Whenever we spend time together, we have a robust discussion about … Continue reading

Posted in Uncategorized
Tagged Alan Turing, commutative law, Gauss, Jack Edmonds, Peano arithmetic, Poincare, Ron Aharoni, words, Zermelo-Fraenkel set theory
3 Comments

## The commutative law

Everybody believes the commutative law for multiplication of natural numbers: for any two natural numbers m and n, we have m × n = n × m. But even professional mathematicians have heated debates about exactly what counts as a proof of this law. Here are … Continue reading