Real number classification

In Real Analysis you study real numbers and their properties.

The classification of real numbers (using set notation) goes like this:

There are also a few others but they belong to more advanced treatments of number theory. Because of these definitions, some numbers may belong to multiple groups. Below is a diagram of these categories.

Fig 1. Classifying real numbers

These numbers have a bunch of properties that are useful shortcuts when doing calculations by hand.

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