# Counting

action of finding the number of elements of a finite set of objects

Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term enumeration refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element.

## Quotes

• 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 in the kitchen;
Seventeen, eighteen, maids in waiting;
Nineteen, twenty, my plate's empty.
• The king was in his counting-house,
Counting out his money;
• Ford carried on counting quietly. This is about the most aggressive thing you can do to a computer, the equivalent of going up to a human being and saying “Blood...blood...blood...blood...”
• If thou dost the number know
Of the leaves on every bough,
If thou can’st the reckoning keep
Of the sands within the deep;
Thee of all men will I take,
And my Love’s accomptant make.
• Anacreontea, 14
• Sir Thomas Stanley, "The Accompt", Poems (1652)
• Sooner may you count the starres,
And number hayle downe pouring,
Tell the Osiers of the Temmes,
Or Goodwins' Sands devouring,
Then the thicke-showr’d kisses here
Which now thy tyred lips must beare.
• Can there be any day but this,
Though many sunnes to shine endeavour?
We count three hundred, but we misse:
There is but one, and that one ever.
• Whoe’er the number would define
Of sports and joys that shall be thine,
He first must count the grains of sand
And every star and twinkling light
That stud the glistening arch of night.
• In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.