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Word Gems 

exploring self-realization, sacred personhood, and full humanity

 

Editor’s collection of notes:

Pre-Algebra

Numbers: Cardinal, Ordinal, Nominal

 

 

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some of the following is from math.net.

 

Cardinal numbers

A cardinal number is used to represent how many of something there are in a group. Cardinality is studied as a part of set theory.

(Cardinal numbers speak to the size of a group or set.)

Given the set A = {1, 2, 3}, there are 3 elements, so the cardinal number is n(A) = 3. Another way to say this is that the cardinality of the set is 3.

Example:

Given the following sets of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}, determine the cardinality of each set.

Although the numbers in each set of numbers above are different, they all have the same cardinality: 3.

We can also count that there are 4 sets of 3 numbers; 4 is another cardinal number.

 

Editor’s note: Here is a math symbol “aleph-null,” representing the smallest of infinities.

 

(See the article on different sizes of infinities.)

And we sometimes hear the idea of “infinity” as a number, that is, a counting number, the "largest" number. But this is incorrect.

Aleph-null is not a counting number, it's a cardinal number indicating the size of an infinite set.

 

 

 

Ordinal Numbers

Ordinal numbers tell us something about order, rank, or position. They can be identified by using terms such as first, second, third, and fourth.

 

Nominal Numbers

Used only for identification purposes, not for counting. 

For example, basketball players might have numerals on their jerseys of "78" or "56" or "23". These numbers tell us nothing about the size of the team or the like but these "nominal numbers" are used only to designate one player from another. "Nominal" means "name" and they're used for naming.