👉 Carpet math is a fascinating concept that bridges geometry and number theory, specifically focusing on the properties of infinite sets and their cardinalities. Imagine a carpet with an infinite number of squares, each square representing a point in a continuum. The "cardioid" carpet, named after mathematician Karl Weierstrass, is a particular type where each square is a circle that fits perfectly around the edges of the carpet without any gaps or overlaps. The beauty of carpet math lies in its ability to demonstrate that some infinite sets, like the set of real numbers, are "larger" than others, such as the set of natural numbers, despite both being infinite. This is achieved through a process called Cantor's diagonal argument, showing that there's no one-to-one correspondence between these sets, leading to the conclusion that the real numbers form a "larger" infinity than the natural numbers.
