02/08/2009, 10:53 PM

tommy1729 Wrote:but some people always insist on

a + b

a * b

a ^ b

which is wrong.

Its not wrong its a different hierarchy.

It follows the pattern: a[n+1](b+1)=a[n](a[n+1]b)

where [n] is the the nth operation.

For example:

a[2](b+1)=a[1](a[2]b) which corresponds to a*(b+1)=a+a*b

a[3](b+1)=a[2](a[3]b) which corresponds to a^(b+1)=a*(a^b)

and so tetration [4] satisfies:

a[4](b+1)=a[3](a[4]b)