Under the pairing n -> 2n, which even number pairs with 12?

Answer: ______________

The bijection n -> 2n pairs naturals with evens. Where does 7 go?

• 7
• 14
• 49
• 9

The doubling rule n to 2n pairs naturals with evens. Where does 7 go?

• 7
• 49
• 14

A proper subset can pair perfectly with its whole set even for finite sets.

Circle one:   True   False

With the add 1 diagonal rule, r1 = 0.305..., r2 = 0.471..., r3 = 0.689.... Give the first three decimals of the new number as one decimal, e.g. 0.123.

Answer: ______________

In the hotel story every guest moves from room n to room n plus 1. Where does the guest in room 5 go?

Answer: ______________

Listed decimals start r1 = 0.141..., r2 = 0.718..., r3 = 0.502.... Using add 1 per diagonal digit (no 9s here), which begins the diagonal number?

• 0.223...
• 0.112...
• 0.141...
• 0.718...

Listing the rationals as a sequence shows they are countable. True or false?

Circle one:   True   False

The diagonal number differs from entry n in digit n. What follows?

• The list contains every real
• The list cannot contain every real
• Diagonalisation enumerates the reals

The diagonal number differs from r_n in digit n. What follows?

• the list contains every real
• the diagonal number must be rational
• the list cannot contain every real
• diagonalisation enumerates the reals