One of the most important mathematical objects is the set, with its many useful properties.
We can look at the size of the set by wondering how many members it contains. The answer obviously can be found by counting them.
Then we can take another set and compare its size with the first one, again by counting the members. We call this size the cardinality of the set.

One can wonder, do I have as many fingers on my left hand as on my right hand?
Well, by counting first left and then right, we find that our hands have an equal number of fingers. But there are or have been primitive cultures that couldn’t count beyond three. Now what? Continue reading →