Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Iterating general commutative operations

  1. Feb 12, 2009 #1
    So multiplication is an iteration of addition and exponentiation is the iteration of multiplication, i.e. a "second" iteration of multiplication (let's say it's a "right-iteration", i.e. (a+(a+a))). Addition is commutative, its first iteration is commutative, but its second iteration isn't. My question is: given an arbitrary commutative operation @, if we continue iterating it, do we always eventually get a non-commutative operation? If no, is there a fixed n such that for some i<n, the i-th iteration of every commutative operation is non-commutative?

    (For a*b+2 and a^b + b^a, the first iteration is already non-commutative.)

    Also, is it possible to obtain a commutative operation by iterating a non-commutative one?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?