A Look at the 20th Century History of the Real Numbers from Cantor to Cohen/Scott/Solovay.

Initial Questions (pre-test)

What is a counting number? a natural number? an integer?

What is the likelihood (probability) of choosing a counting number at random from all the integers between -10 and 10?

What is a rational number? an algebraic number? a real number?

What is the likelihood (probability) of choosing a counting number at random from all the rational numbers between -10 and 10?

What is the likelihood (probability) of choosing a rational number from all the real numbers between -10 and 10?

Arrange the following sets of numbers from smallest to
largest:

natural numbers | algebraic real numbers | integers |

real numbers | transcendental real numbers | rational numbers |