Re: Power Question

On Jan 6, 4:39 pm, David W. Cantrell <DWCantr...@xxxxxxxxxxx> wrote:
"Dana" <ddelo...@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


mathematicians usually use

c
b
a

which presumably does not mean the same as

bc
a

or they would write it that way.

I doubt that you would find much use of the "^" symbol outside of
computer programs, so it is a computer language question more than a
math question. There are people who establish standard for computer
languages. Sometimes it is the designer, and sometimes it is some
committee. e.g. a subcommittee of ANSI.
.