It certainly does not render reckoning with

cardinal numbers possible It does not open a field for economic calculation and the mental operations based upon such calculation.

Count all the

cardinal number names spelt with a given number of letters.

In the case of common fractions, the words used to describe numerators follow the pattern of

cardinal numbers. However, when describing denominators, the words follow the pattern of ordinal numbers, but with exceptions for the words half (plural halves) to describe a denominator of two and quarter for the denominator four.

An Ordinal Scale can never produce a series of

cardinal numbers (Arrow).

In a similar way, we form the set of all US states, and we say that the

cardinal number of this set is 50.

Problem 4.2 For which numbers k, n are the

cardinal numbers [c.sub.k] ([H.sup.n]) and [c.sup.B.sub.k] ([H.sup.n]) finite?

If [alpha] = [absolute value of A] and [beta] = [absolute value of B] are

cardinal numbers such that there is an injection from A to B we say that [alpha] is smaller than [beta]; if, further, the sets A, B are not equipotent, we say that [alpha] is strictly less than [beta] and we write [alpha] [??] [beta].

The method that Cantor introduced to directly generate new infinite

cardinal numbers is via the use of the power set function.

In addition to Emanuel Schongut's lovely illustrations, "Christmas Eve Blizzard" is enhanced for young readers with a Spanish/English glossary for the Spanish words that appear in the text of the story, as well as fun facts about birds (and cardinals in particular), information on making a bird-friendly backyard habitat, easy bird feeder crafts for Christmas and year round, information on what to do if the young reader were to find an injured or orphaned baby bird, and even

cardinal numbers and math games!

This analogy is unsatisfactory because it reduces the complex, emergent relatedness of the order of the universe to a mere collection of countable items, and it construes God as the concept of a transfinite

cardinal number. But transfinite

cardinal numbers are directly understandable by human minds (though this requires considerable effort), whereas God surpasses all direct human understanding.

What entities make "There are infinitely many transfinite

cardinal numbers" true?