Tag Archives: equivalence relations

Equivalence relations, 2

I believe, and have said in earlier posts here and here on this blog, that the Equivalence Relation Theorem is the modern pons asinorum, the bridge which you must cross in order to become a mathematician: it is essential to … Continue reading

Posted in doing mathematics | Tagged , , , | 7 Comments

Mathematical Structures, 6

The main topic this week was integers, divisibility, and Euclid’s algorithm for greatest common divisor. How do you construct the integers from the natural numbers? There are two ways: You could say that Z = N∪{0}∪{−n:n∈N}. That is, an integer is either … Continue reading

Posted in exposition, teaching | Tagged , | 6 Comments