11/06/2011, 08:06 PM

I realize now we have to create a second axiom in order that the series of operators become the true Ackermann function.

Consider the possibility that:

we still have the result that

the only difference is that

and in return we get

So in order to get the true Ackermann function we must make the second assertion:

This is actually the equivalent to the iteration axiom:

though only true for integer values of sigma greater than or equal to two.

Therefore we define the Ackermann function from axioms:

such that

Does anyone see any modifications necessary?

Consider the possibility that:

we still have the result that

the only difference is that

and in return we get

So in order to get the true Ackermann function we must make the second assertion:

This is actually the equivalent to the iteration axiom:

though only true for integer values of sigma greater than or equal to two.

Therefore we define the Ackermann function from axioms:

such that

Does anyone see any modifications necessary?