Determine the cardinality of an infinitely large set.

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Before entering into a definition of what a cardinal number is, we must first introduce rules relating the size of sets.

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Cardinality problem

How do I determine the cardinality of an infinitely large set (such as real numbers)? What is c and 2^c mean?

Answer:

Here are some aspects which will clarify some thoughts on this matter:

Man had to compare various sets of things, for example, flints, dogs and hunting companions, in order to ascertain which set contains more elements (constituents, members). Today one does this as a rule, by counting and comparing the quantities obtained. This presumes an ability to count, that is, knowledge of the numbers. But there is an easier way if one wishes to find out. For example, whether men and horses are present in equal numbers, one simply places a rider on every horse. In other words: one sets up a matching, a correspondence, between men and horses. This matching may tally, ...