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The set of Real numbers includes all commonly used numbers. But the Real numbers are only a proper subset of the set of Complex numbers, and the Complex numbers are a proper subset of Quaternions.


It is a bit like the Russian Babushka dolls with one doll inside another which is inside another, and so on. In reality, therefore, there is no such set.


Also, note that "Group" has a very special meaning in mathematics. The set of Real numbers is a group, but it is also a Field.

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10y ago

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