Posted by T.Gracken on October 30, 2002 at 20:04:13:
In Reply to: Re: order of operations posted by Joel on October 30, 2002 at 19:27:42:
: : : Just want to be sure...
: : : a^b^c is evaluated as (a^b)^c = a^(bc), correct?
: : this is one of those "sticky" situations. Like 'definitions'
: : I tend to look at this as (precisely) per order of operations and (reading left to right) since "a" has an exponent, we must determine the exponents value and its value is (b^c). This is easily argued as something else... which is easily argued as this... which is...
: : Many people see it exactly as you do.
: : So, unless grouping symbols are included with the original expression, it is one of those 'un-winnable' debates.
: : that is, parties discussing this expression must agree on (or accept) the notation if anything further is to be agreed upon.
: : personally, I have no problem either way; as long as I know what the other person interprets as.
: : ...of course, there are (many) organizations (all of whom claim to be the most accepted) that will claim their decision is the correct one.
: OK - so your interpretation is to evaluate it as a^(b^c)?
: That works for me. :)
: I'm working on a problem that was given with no parentheses and didn't make sense the way I was interpreting it. Your way, it does.
: I just thought that since it involves two instances of the same operator, the precedence was equal and should be evaluated left to right.
like I said, it depends on who you discuss this with. some will be extrememly biased. I just got tired of the arguements and made it a habit of asking "what is your opinion/preference/belief/etc.?".
It really is one of the most disputed (and silly) 'notation' problems among (psuedo) mathematicians.
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