CSCI 1240: The Computational World Problem Set 1: Week 1 ...

a. The set of all rational numbers between 0 and 0.001
b. The set of all irrational numbers between 0 and 0.001
c. The set of all distinct ways of ordering a deck of 52 cards.
d. The set of all possible ways of assigning either 0 or 1 to 40 distinct slots. (Another way
of thinking of this: imagine 40 blanks. How many distinct binary numbers can you write
in those 40 blanks?)
e. The set of all possible ways of assigning either 0 or 1 to a countably infinite number of
slots. (Another way of thinking about this: how many possible infinite-length binary
numbers can you write?)
f. The set of all perfect squares (1, 4, 9, 16…).
g. The set of all distinct pairs from an overall set of 100 items. (Another way of thinking
of this: there are 100 people in a room. How many distinct handshakes are possible?)
h. The set of all points in the interior of a unit circle (the circle of radius 1).
i. The set of all possible (syntactically correct) Turing machine programs that can be
written in at most 500 standard alphabetic characters.
j. The set of all possible programs for a Turing machine.