Wacław Sierpiński in the context of "Sierpiński carpet"

In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets. The term transfinite was coined in 1895 by Georg Cantor, who wished to avoid some of the implications of the word infinite. In particular he believed that "truly infinite" is a perfect and thus divine quality and so refused to attribute this term to mathematical constructs comprehensible by humans. Few contemporary writers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as infinite numbers. Nevertheless, the term transfinite also remains in use.

Notable work on transfinite numbers was done by Wacław Sierpiński: Leçons sur les nombres transfinis (1928 book) much expanded into Cardinal and Ordinal Numbers (1958, 2nd ed. 1965).

The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński but appeared as a decorative pattern many centuries before the work of Sierpiński.