News for hackers. Stuff that matters.

A comment on The existence of the square root of two (2001).

Re:The existence of the square root of two (2001) by pfortuny on Monday December 25, 2017 @06:51AM (#16003793)
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.

[ Parent | on HN ]
Re:The existence of the square root of two (2001) by bjourne on Monday December 25, 2017 @10:47AM (#16004494)
Your 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.
[ Parent | on HN ]
Re:The existence of the square root of two (2001) by OscarCunningham on Monday December 25, 2017 @09:12AM (#16004128)
He's actually exploring the difficulties of defining numbers numbers in a naive way to be their decimal expansions.
[ Parent | on HN ]
Re:The existence of the square root of two (2001) by nyc111 on Monday December 25, 2017 @12:25PM (#16004888)
But 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.
[ Parent | on HN ]