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 \(0\)s and \(1\)s. The bus has every person named with every possible infinite sequence of \(0\)s and \(1\)s, 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.