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

Re:The existence of the square root of two (2001) by adrianN on Monday December 25, 2017 @08:21AM (#16003990)
The irrationality of sqrt(2) was known to Pythagoras.
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Re:The existence of the square root of two (2001) by infinity0 on Monday December 25, 2017 @08:43AM (#16004045)
You missed the point of the post. Pythagoras could prove sqrt(2) is irrational but the proof already implicitly assumes it exists.

"exists" in mathematics, basically means that it does not contradict the axioms of whatever system you're working under, or result in a logical inconsistency. For example, the set that is the subject of Russell's paradox, cannot exist in any reasonable system of set theory, and its definition shows that naive set theories are logically unsound.

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Re:The existence of the square root of two (2001) by adrianN on Monday December 25, 2017 @01:47PM (#16005223)
No, Pythagoras started from something that definitely exists: the hypotenuse of a triangle with two sides of length 1. He wanted to find out its length and to his great dismay he discovered that there is no rational number to express its length.
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Re:The existence of the square root of two (2001) by sebapi747 on Saturday December 30, 2017 @09:19PM (#16038983)
You don’t need Euclidean space to exist to define reals but you need reals numbers for distance to exist.
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