Theoretical analysis defines cardinal numbers through cluster formation of identical entities, suggesting an alternative axiomatic foundation for elementary counting.
Definition It is a thing. They are things. Definition 1. A cardinal number is a thing that makes the thing into a cluster or that makes the things into a cluster. The things are identical to one another. In definition 1, the first cluster is a self-cluster, which the thing forms. A thing and a thing are not two things. In a thing and a thing, each thing is selected. However, each thing is not a cluster. Two things are a cluster.
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