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Archimedes had that conceptual argument, but the modern definition is based on a lot of math Archimedes didn't have, including model theory and the algebra of o
by psychometry 13y ago
Archimedes had that conceptual argument, but the modern definition is based on a lot of math Archimedes didn't have, including model theory and the algebra of ordered fields.
- pdonis 13y agoYes, but do you need the modern definition to do calculus, in a practical sense? I don't think so. The way things actually went, practical computations using calculus, by Newton and others, came a couple of centuries, at least, before the modern rigorous foundations were developed. So if some other development had intervened, in the sort of alternate history postulated in the article, to prevent the practical computations from being taken further, that could have prevented the modern rigorous foundations of calculus from being developed. To put it another way, if other developments had not intervened, the next couple of centuries after Archimedes could possibly have seen something like our modern rigorous foundations for calculus being developed.