This was not well understood at that times, but the fact that infinity occurred in the definition of the natural numbers was a problem for many mathematicians of this time. For example, Henri Poincaré stated that axioms can only be demonstrated in their finite application, and concluded that it is "the power of the mind" which allows conceiving of the indefinite repetition of the same act. This applies in particular to the use of the last Peano axiom for showing that the successor function generates all natural numbers. Also, Leopold Kronecker said "God made the integers, all else is the work of man". This may be interpreted as "the integers cannot be mathematically defined".
Thi,s was not well understood at that times, but the fact that infinity occurred in the definition of the natural numbers was a problem for many mathematicians of this time. For example, Henri Poincaré stated that axioms can only be demonstrated in their finite application, and concluded that it is "the power of the mind" which allows conceiving of the indefinite repetition of the same act. This applies in particular to the use of the last Peano axiom for showing that the successor function generates all natural numbers. Also Leopold Kronecker said "God made the integers, all else is the work of man". This may be interpreted as "the integers cannot be mathematically defined".