What are numbers?
Numbers are the central object of study in mathematics. Most humans, and certainly all humans in modern, industrial societies, are familiar with numbers and, indeed, use them regularly in their daily...
View ArticleDefinitions of finiteness
Perhaps the most intuitive definition of finiteness as a property of sets is that a set is finite if and only if its cardinality is a natural number. Unfortunately, the most intuitive definition of the...
View ArticleSet isomorphisms
There doesn’t seem to be any standard adjective to describe the property of a pair of sets having the same cardinality. Some authors use ‘equivalent’, but this adjective could be used for any...
View ArticleAn introduction to the cardinal numbers
There are lots of different kinds of numbers. In school, you learn about some of them: integers, rational numbers, irrational numbers, real numbers, imaginary numbers, complex numbers. So educated...
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