A function question

[MathStudent1999]

A function A(x,y) is defined by the following rules:

A(0,n) = n+1
A(m, 0) = A(m-1, 1)
A(m, n) = A(m-1, A(m, n-1))

for m and n natural numbers.

A(2,3)= k where k is a whole number. Find the value of k.

I just plugged 2, and 3 into the third formula and kept of simplifying. 10 came out at the end. Is there a easier way to do this problem?

 

[stapel]

A function A(x,y) is defined by the following rules:

A(0,n) = n+1
A(m, 0) = A(m, n-1)
A(m, n) = A(m-1, A(m, n-1))

for m and n natural numbers.

Are you sure about that second rule, the one for A(m, 0)? Since that one doesn't include "n" in the input, I'm not seeing how one is supposed to get something in terms of "n" as an output.

 

[MathStudent1999]

Are you sure about that second rule, the one for A(m, 0)? Since that one doesn't include "n" in the input, I'm not seeing how one is supposed to get something in terms of "n" as an output.

Sorry, it's supposed to be A(m, 0) = A(m-1, 1)

 

[stapel]

Thank you for the correction.

No, I don't think there's a simpler way to do this. It's just painful. I come up with "8", though. If you keep coming up with 10, please reply showing your steps, and I'll show mine. Thank you!