Problem #WSP-5263

Problems Discrete Mathematics Set theory and logic Set theory

Problem

Imagine you see a really huge party bus pulling out, an infinite bus with no seats. Instead everyone on board is identified by their unique name, which is an infinite sequence of 0s and 1s. The bus has every person named with every possible infinite sequence of 0s and 1s, someone is named 00010000..00..., someone else 0101010101..., and so on. Prove that this time you will not be able to accommodate all the new guests no matter how hard you try.