[emergie]

"Split" means that you have defined division, which implies having rational numbers.

In the beginning there were only Natural numbers.

-1 appeared the moment one decided to define complementary operation to addition. -1 in reality is only a shorthand for "0-1", 0 comes here as neutral element of addition. Addition is well defined on Natural numbers. Subtraction generates Zahl numbers.

Similarly multiplication is well defined on Zahl numbers. It's the complementary operation - division - that generates Quotient/rational numbers.