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It seems he confuses a quantinty with its numerical expression. The square root of 2 is just the length of a segment: the diagonal of a square of side 1. As lon
by pfortuny 9y ago
It seems he confuses a quantinty with its numerical expression. The square root of 2 is just the length of a segment: the diagonal of a square of side 1. As long as “square, side and 1” are allowed to “exist”, sqrt(1) does exist.
No, you cannot write its decimal expansion. But neither can you that of 20/7. However, its continued fraction is trivial.
- OscarCunningham 9y agoHe's actually exploring the difficulties of defining numbers numbers in a naive way to be their decimal expansions.
- bjourne 9y agoYour argument rests on the notion of "length" which you don't get for free. :) You won't be able to define "length" without assuming the existence of irrational numbers.
- nyc111 9y agoBut in this sense, the length of the diagonal exists but you cannot measure it with your chosen unit which is the side of the square. If you take the diagonal as your unit you cannot measure the side either.