19. The infinite
In the Middle Ages the problem of infinity was of interest mainly in connection with arguments about whether the set of angels who could sit on the head of a pin was infinite or not.
N. Ya. Vilenkin, Stories about Sets (1965)
… the true mathematician and physicist know very well that the realms of the small and the great often obey quite different rules.
Kurt Singer, Mirror, Sword and Jewel (1973)
TOPICS: Set theory, cardinal and ordinal numbers; König’s Infinity Lemma, Zorn’s Lemma and equivalents; infinite Ramsey Theorem; the ‘random graph’
TECHNIQUES: Transfinite induction; free constructions; back-and- forth; probabilistic ...