Problem #PRU-60552

Problems Algebra Number theory. Divisibility Divisibility of a number. General properties Calculus Real numbers Integer and fractional parts. Archimedean property
 12–14  2.0

Problem

Prove that for a real positive \(\alpha\) and a positive integer \(d\), \(\lfloor \alpha / d\rfloor = \lfloor \lfloor \alpha\rfloor / d\rfloor\) is always satisfied.