# Can computers deal with infinite objects in finite time?

## Martin Escardo, University of Birmingham

For example, can they calculate with real numbers represented as infinite sequences of digits, so that all digits printed at any given time will be correct, and so that they print digit after digit in a never ending fashion? Can they check an infinite number of possibilities and answer yes or no after calculating for a finite amount of time?

Sometimes they can, and sometimes they cannot. And sometimes we are able to tell whether they can or cannot. I will explore the mathematical tools and foundations for computing with infinite objects, including general topology and constructive logic (and excluding many useful branches of mathematics that time will not permit to cover). There will be theory and examples.