Re: Power Question

"Dana" <ddelouis@xxxxxxxxxxxxx> wrote:
Does anybody know of a reference to the following question?
What is the proper interpretation of a^b^c ?

I understand that there may not actually be a "proper" interpretation,

There isn't.

and it is left up to each program.

Example:
2^3^4

Excel reads it left-to-right to return 4096.

I'm told Maple 11 says it's ambiguous, and that we should use
Parenthesis.

Although we should always strive to be unambiguous, there's nothing wrong
with a program, like Mathematica, deciding on a specific interpretation of
a^b^c.

Other programs, like Mathematica, read it right-to-left and returns
2.417*^24.

Anyone know of any reference for a "ruling," or is it just a case of
"each program is different."

How could there be such a ruling? Who would make it? (E.g., I suppose a
body such as the DIN could make such a ruling, but would it have much
influence outside of Germany?) Mathematicians, much to my regret, do not
have any standardizing agency.

BTW, one argument for taking a^b^c to mean a^(b^c) is that, if we actually
want (a^b)^c, it can be written easily, via a law of exponents, as a^(b*c).

David
.

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