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Re: Please remind me why -3^2 = -9
Posted:
Nov 18, 2012 7:44 PM
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On Nov 18, 2012, at 10:00 AM, Phil Mahler wrote:
> And that no student will properly misinterpret 7 - 3^2, but the
> problem is the isolated -3^2. Significantly, with no space after the
> hyphen.
The difficulty is that, as mentioned before, there is lot missing that
goes without saying (and which iI have written within square bracket).
If, as we should, we expect integers and do not allow "positive" to go
without saying, then 7 - 3^2 is ill-formed and it is not surprising
that we should have
[+]7 ominus [+]3 ^2 = +7 ominus +3 ? +3 = +7 ominus +9 = +7 oplus -9
= -2
versus
[+]7 (oplus) -3 ^2 = +7 oplus -3 ? -3 = +7 oplus +9 = +16
More generally, the trouble is that we write a lot of shorthand
without much delving on the longhand and dealing explicitly with the
default rules.
Regards
--schremmer
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