Love is infinite. The joy of children is infinite. These notions come to mind when we think of infinity. Mathematics, however, reveals further, initially hidden perspectives.

It turns out that the well-known number line from school is not the final word of wisdom: after 1, 2, and 3, after a million and a trillion, after the number of grains of sand – after all these numbers, infinitely large numbers follow. Astonishingly, we humans, despite our limited minds, can explore this infinite hierarchy of large numbers and gain reliable information about them.

In this talk we will learn how to visualize and compute with these infinitely large numbers. (This part of the talk will be similar to an earlier version of this talk given at 35c3.)

Then we will go on a tour of varied applications of those infinitely large numbers: There are problems which, provably so, can only be solved by appealing to the infinite.

Surprisingly, one of these applications is in algorithm design.

In order to enjoy the talk, absolutely no mathematical prerequisites are needed: The talk is even accessible to school children of age ten and above (if they understand English). And still it is mathematically rigorous – we'll learn how to think about and compute with infinities in a precise fashion. After the talk you'll be able to effortlessly converse on infinitely large numbers with your mates.

There will also be a companion talk on very large but still finite numbers. This talk is not a prerequisite for the other, and vice versa.

Here is a list of more sessions by our group.

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