>>6222
this is an idea addressed by combinatorics
also to answer your question about natural numbers being defined without infinity, you can expression natural numbers as either 0 or the successor of a natural number
for example, 4 would be defined/encoded as successor(successor(successor(successor(0)))), which can be extended ad infinitum
you also have von neumann natural numbers where natural numbers are sets and their cardinality encodes their value, eg, ø = 0, {ø} = 1, {ø, {ø}} = 2, {ø, {ø}, {ø, {ø}}} = 3 and so on
also if you wanna be extra fancy, natural numbers can also be defined by church encoding and beta-reduction, λα.λβ.λγ.M can be reduced 3 times therefore it encodes 3, M itself cannot be reduced (atleast, we assume) therefore it encodes 0, if we suppose we have abstraction binding (like f := λx.M) we can encode infinity using infinite recursion and self applying abstractions
