See ~ page 16 here for the (historic) definition: https://personal.math.ubc.ca/~cass/courses/m446-05b/dedekind-book.pdf https://personal.math.ubc.ca/~cass/cour

See ~ page 16 here for the (historic) definition: https://personal.math.ubc.ca/~cass/courses/m446-05b/dedekind-book.pdf https://personal.math.ubc.ca/~cass/courses/m446-05b/dedekind... It’s possible to work with both {x : x < r} and {x : x <= r} and maintain the distinction between 0.999… and 1, but then eg. 1 = 0.999… + x has no solution.