Dedekind Cuts

Dedekind cuts are a way to define real numbers mathematically by dividing the set of rational numbers into two non-empty parts with specific properties. Imagine listing all rational numbers less than a certain value; this collection forms a "cut." The lower part contains all numbers less than that real number, and the upper part contains all numbers greater or equal. This method allows us to precisely define irrationals (like √2) as the "cut" that separates all rationals smaller than √2 from those larger, creating a continuous number line that includes both rationals and irrationals.