Counting

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.

• 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.
  • "One, Two, Buckle My Shoe"
  • Variant: Nineteen, twenty, / My belly's empty.

• The king was in his counting-house,
    Counting out his money;
  • "Sing a Song of Sixpence"
  • Variant: The king was in the parlour, / Counting o’er 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...”
  • Douglas Adams, The Hitchhiker's Guide to the Galaxy (1979)

• 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.
  • Thomas Campion, Two Bookes of Ayres, II (1613), no. 18

• 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.
  • George Herbert, "Easter", The Temple (1633)

• Whoe’er the number would define
  Of sports and joys that shall be thine,
  He first must count the grains of sand
  That spread the Erythræan strand,
  And every star and twinkling light
  That stud the glistening arch of night.
  • Catullus, Carmina, 61
  • Leigh Hunt, in The Examiner (12 May 1816)

• 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.
  • Stanisław Lem, Cyberiada (1965)
  • Michael Kandel, tr., The Cyberiad (1975)

• Count the bees that on Hybla are playing,
    Count the flow’rs that enamel its fields,
  Count the flocks that on Tempe are straying,
    Or the grain that rich Sicily yields;
  Go number the stars in the heaven,
    Count how many sands on the shore,
  When so many kisses you’ve given
    I still shall be craving for more.
  • Martial, Epigrams, 6, 24
  • Sir Charles Hanbury Williams, in Dodsley’s Collection, IV (1755)

• Let’s number out the hours by blisses,
  And count the minutes by our kisses;
  • Jasper Mayne, The Amorous War (1648)

• When I do count the clock that tells the time,
  • William Shakespeare, Sonnets, 12

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Counting