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Ordinal numbers indicate the position of something in a sequence. They are similar to cardinal numbers, but with added letters. Georg Cantor invented them in 1897 as part of set theory. Ordinal numbers are commonly used to count places and grade levels.
An ordinal number is a number that indicates where in sequence something is related to another number or object. In English, an ordinal number is different from other types of numbers in that there are usually a couple of letters added to the root word to produce the ordinal number. However, most ordinal numbers are very similar to their cardinal number counterparts. For example, cardinal numbers are one, two, three, and so on. Ordinal numbers are first, second, third, and so on.
Ordinal numbers were invented by Georg Cantor in 1897, a German mathematician born in Russia. He is probably best known for inventing set theory. Set theory basically explains that numbers can function as a set and that there could be numbers common to both sets. For example, if there is a set {1,2,3} and a set {2,3,4}, the common numbers between them would be {2,3}. Common numbers are called intersection of sets.
There are also a number of other operations that go hand in hand with set theory. Set theory also allows the number zero to be included as a natural number. The number zero is the only natural number that cannot be an ordinal number.
An ordinal number is commonly used in English when describing the relationship of natural numbers. Natural numbers are counting numbers, or the traditional numbers we think of in mathematics. They are also called count numbers. An ordinal number can be treated like a cardinal number, and therefore is subject to any mathematical calculation. However, an ordinal number is not commonly used in mathematical calculations, except perhaps at the end of the calculation.
Ordinal numbers are also very similar to integers, which include both natural numbers and their negative counterparts. However, an ordinal number is never used in the negative form. Therefore, since there are no ordinal numbers that represent negative numbers or zero, it is logical to conclude that ordinal numbers represent only positive integers.
In modern usage, ordinal numbers are mostly used to count places. For example, if a group finished a race, the top three we would say finished first, second and third. The next three will finish fourth, fifth and sixth. In school, this is a common way to refer to grade levels.
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