# Tetration induction proof

Problem picture

Picture of given ackermann function So far, I have $$A(3,n) = A(2,A(3,n-1))$$ and then using $$A(2,n) = 2 \uparrow \uparrow n$$ I arrive at. $$A(3,n) = 2 \uparrow \uparrow A(3,n-1)$$ I'm not clear how to proceed from this point to rewrite it as a triple arrow function. Thank you for any help

• It looks like you're almost there... Look at the form of your function, and at the form of the triple arrow $$a \uparrow \uparrow \uparrow k = a \uparrow \uparrow (a \uparrow \uparrow \uparrow (k-1))$$. – Matt Groff Oct 31 at 23:37