I said either associative or parenthesized. People don't write a/b/c because they had 10 years of learning to use parens in arithmetic, but they write f a b all

I said either associative or parenthesized. People don't write a/b/c because they had 10 years of learning to use parens in arithmetic, but they write f a b all the time. For the same reason, my rule of thumb applies only to operators that you define. The non-associativity of exponentiation does throw people off sometimes. Not all college students will correctly parse 2^2^2. IMO it's a wart in math notation. It could've been easily avoided by e.g. drawing a box around the exponent, so stacked exponentials would have boxes nesting upward.