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What Are the Differences Between Cardinal Numbers and Ordinal Numbers?

People have used abstract numbers, such as tally marks to keep track of time, since prehistoric times. Western digits, otherwise known as Hindi-Arabic, date back to at least the fifth century in Rome, when first used on an Abacus. Cardinal and ordinal numbers are part of "Set Theory," developed by Georg Cantor in 1897 to classify sets and account for infinite sequences.
  1. Quantification

    • While Cardinal numbers are used to quantify things, such as to describe "how many" there are of something, ordinal numbers do not quantify anything.

    Order

    • Ordinal numbers are used to denote placement or order, whereas Cardinal numbers do not indicate order. If an item is fifth in a list, then "fifth" would be its ordinal number.

    Inclusion

    • Cardinal numbers can become ordinal numbers by placing them in a list, but ordinal numbers cannot become cardinal numbers, because they are by definition place indicators and not sums. For example, if there is a total sum of five dogs (five being a cardinal number), then by saying "dog number five is brown," this turns the cardinal number into an ordinal number as well. Using the ordinal number in the same case, however, would not make it a cardinal number as well. For example, by saying "the fifth dog is brown," the ordinal number does not become a cardinal number.

    Prefixes

    • Both cardinal and ordinal number series have their own set of Latin-derived and Greek-derived prefixes. Cardinal prefixes include semi (meaning half or partial in Latin), hemi (meaning half in Greek), tri (meaning three in Latin and Greek), sexa (meaning six in Latin) and hexa (meaning six in Greek). Ordinal prefixes include prim (meaning first in Latin), terti (meaning third in Latin), quart (meaning fourth in Latin) and sext (meaning sixth in Latin).

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