finite satisfiability of 0 is not successor and successors of distinct numbers are distinct

In Edit [Moderator]: Link removed it says that:

Indeed, the conjunction of the following two propositions is not satisfiable in any finite universe of discourse.
1) Zero is not the successor of any number.
2) Every two numbers which are successors respectively of distinct numbers are themselves distinct.

Which, according to my understanding of wikipedia, means, that there is no finite model for which both of these propositions are true. But I don't see any problem for any finite universe. Can anyone explain what I'm missing?