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Dijkstra is arguing in the context of natural numbers, which in the standard naive set-theoretic construction starts with 0.
by joatmon-snoo 10y ago
Dijkstra is arguing in the context of natural numbers, which in the standard naive set-theoretic construction starts with 0.
- thanatropism 10y agoI've only seen naturals start with zero in Calculus 101 books. Any "introduction to real analysis for third-year undergrads" will do 1, at least in my experience.
- joatmon-snoo 10y agoDespite having a math degree, somehow I never took an analysis class, so I can't common on that specifically (I do believe that's one of the places where analysis diverges from other field's conventions; that being said, I do believe it is fairly standard practice to specify whether naturals start from 0 or 1 in a paper). In naive set theory, starting with 1 poses some problems (specifically, you don't have numbers yet, so you start with the notion of the empty set, which you use to define 0, and then proceed from there). Starting the naturals from 0 is also problematic in group theory, since you lose the additive identity.