# Does ternary operations have associative property?

Binary Operation is a function. Right?
We know that all Binary operations have associative property.
They must be either associative or non-associative.
The condition is :
$$(a*b)*c = a*(b*c)$$ $$f(f(a, b), c) = f(a, f(b, c))$$ If this condition is true for all a, b, c combinations then the $"*"$ operation is associative.

Also we know that Unary operations does not have an associative property.
like "!" operation as a factorial of any real number.
We may say it is always associative.

• You're effectively asking for a function s.t. $f(a,b,f(c,d,e)) = f(f(a,b,c),d,e) = f(a,f(b,c,d),e)$. Some functions might satisfy this some might not. Trivial example $f(a,b,c) = a+b+c$ then it's associative. – Dan Oct 7 '13 at 8:44