One, two, buckle my shoe;Three, four, knock at the door; Five, six, pick up sticks; Seven, eight, lay them straight; Nine, ten, a big fat hen. Eleven, twelve, dig and delve; Thirteen, fourteen, maids a-courting; Fifteen, sixteen, maids a-kissing; Seventeen, eighteen, maids a-waiting; Nineteen, twenty, my plate’s empty.
Perhaps the oldest mathematical activity is counting. Some of the earliest words we learn as children are the names of the first few natural numbers and counting games are very common. In this chapter the counting process is formulated mathematically as the constructing of a bijection from a standard set of positive integers to the set of the elements being counted. This allows us to consider precisely ...