Counting

Abstract

The ancient skill of counting is the pairing of objects in one collection with those in another in a one-to-one fashion; sheep might be paired with a particular set of pebbles, for example, to make sure that no sheep has gone astray. Whether by slow progression or in sudden illumination, our ancestors focused their minds on the central idea in this process and, abstracting it, discovered a class of numbers, exactly one of which can be paired with any given set. There are two important characteristics discernible in this abstraction: it exhibits simplißcation in that material objects such as pebbles are no longer needed for counting; and it exhibits generalization in that counting now has an infinitely wider scope of application. These two characteristics are the hallmarks of every true mathematical development.

Nor did the French possess the Salique land Until four hundred one and twenty years After defunct ion of King Pharamond, ... Who died within the year of our redemption Four hundred twenty-six; and Charles the Great Subdu ’d the Saxons, and did seat the French Beyond the river Sala, in the year Eight hundred five. Henry V, I,ii.