[simiones]

1. The kth root of x being x^1/k would be written as this:

  k     1/k
  △x = x△

2. I don't think these are as important. Also, ln x / log x is still the same or more symbols than `e△x`.

3. Not significantly more than parens in exponents. You also get rid of one level of parens from log.

4. Notation change is often a huge hassle, this is absolutely true.

5. Isn't this a problem for current notations as well? Especially if you ever want to put a complex expression for k in the k'th root notation.

6. log_a(log_a(x)) would be `a△(a△x) `.

Still, I don't personally like the symbol. The biggest problem to me is that it requires smaller letters (subscripts/superscripts) all the time, which makes it more annoying to write than the regular notation for the base of an exponentiation and the argument of a log or root. Complex expressions in small letters are very annoying to me, and this notations makes it necessary to use them in all cases, where the normal notation at least has some cases where this is not needed.