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.

But what about Ternary operations?
Do ternary operations have an associative property?
If it has, show me sample please!
How to define a condition of associativity for a Ternary operation?

  • 1
    $\begingroup$ 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. $\endgroup$ – Dan Oct 7 '13 at 8:44
  • $\begingroup$ So do you mean that ternary operations have associative property? $\endgroup$ – IremadzeArchil19910311 Jul 10 '14 at 18:10
  • $\begingroup$ See math.stackexchange.com/questions/94690/… in the answer two generalisations of the associative property are discussed, I'm do not know if either is commonly referred to as the associative property for ternary operations though. $\endgroup$ – Alex J Best Jul 16 '14 at 14:19

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