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Get it mathematically correct.
Dedekind cuts are named after the German mathematician Richard Dedekind (1831-1916).
Dedekind cuts are named after the German mathematician Richard Dedekind (1831-1916).
The problem of the rational numbers is that quantities that seemingly ought to exist, do not exist as rational numbers, even though the rational numbers can get arbitrarily close to what the value should be. Perhaps the simplest such number is the square root of 2. The function f(x) = x<sup>2</sup> passes through the value zero somewhere between 1.414 and 1.415, but never achieves the value zero, when only rational numbers are considered. (See [[real number]] for an outline of the proof that the square root of 2 is irrational.)
The problem of the rational numbers is that quantities that seemingly ought to exist, do not exist as rational numbers, even though the rational numbers can get arbitrarily close to what the value should be. Perhaps the simplest such number is the square root of 2. The function f(x) = x<sup>2</sup> - 2 passes through the value zero somewhere between 1.414 and 1.415, but never achieves the value zero, when only rational numbers are considered. (See [[real number]] for an outline of the proof that the square root of 2 is irrational.)
A Dedekind cut is a subset of the rationals that satisfies:
A Dedekind cut is a subset of the rationals that satisfies: