Ultraintuitionism

In the philosophy of mathematics, ultraintuitionism is an extreme version of intuitionism.

Ultraintuitionists deny the existence of the infinite set N of natural numbers, on the grounds that it can never be completed. In addition, ultraintuitionists are concerned with our own physical restrictions in constructing mathematical objects. Thus some ultraintuitionists will deny the existence of, for example, the floor of the first Skewes' number, which is a huge number defined using the exponential function as exp(exp(exp(79))), or

<math>e^{e^{e^{79}}}.</math>

The reason is that nobody has yet calculated what natural number is the floor of this real number, and it may not even be physically possible to do so.