Isn’t one infinity bigger than the other? That’s the question that Georg Cantor, a German mathematician who died shortly before World War I ended, grappled with throughout his life.

Without the theorem of the excluded middle, all kinds of difficulties arise. In fact, many mathematical proofs are based on this very principle. It is no surprise, then, that only a few mathematicians ...

Furthermore, there are differences even with infinite values: infinity does not always equal infinity. Thus, infinity would not be a guaranteed winner in a largest number contest.

NOVA: How did Georg Cantor's set theory refine mathematicians' thinking about infinity? Netz: Well, the essence of the calculus is that you deal with infinitely large objects.

Cantor proved many startling results. There is not just one infinity, but an entire hierarchy of transfinite quantities, increasing without limit.

Likewise, as Cantor demonstrated, the infinity of all possible rational numbers (numbers that can be expressed as the ratios of two integers) is also the size of the first aleph.

Infinity is bigger than any number. But saying just how much bigger is not so simple. In fact, infinity comes in infinitely many different sizes—a fact discovered by Georg Cantor in the late ...

Yes, infinity comes in many sizes. In 1873, the German mathematician Georg Cantor shook math to the core when he discovered that the “real” numbers that fill the number line — most with never-ending ...

The theory of infinite sets was developed in the late nineteenth century by the brilliant mathematician Georg Cantor. Many of Cantor's ideas and theorems sit at the foundation of modern mathematics.

Many levels of infinity The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it WHEN David Hilbert left the podium at the Sorbonne in Paris ...

You can’t get any bigger than infinite, right? Well, kind of. Late in the 19th century, German mathematician Georg Cantor showed that infinite comes in different types and sizes. Scientific ...