negative number raised to even power

[Manolo Sobrino]

(05-07-2015 05:50 PM)Dave Britten Wrote:  Then I disagree with "standard mathematical notation". If -2^2=-4, then as far as I'm concened, 2.5^2=2.25 is just as valid.

OK, -2 belongs to Z, (Z;+;*) is a (unitary and commutative) ring.

When I'm reading an expression and someone wrote (-2)^2, it means (-2)*(-2). They're squaring -2 ∈ Z. I get 4.

When it's -2^2, it means someone squared 2 ∈ Z and then considered it's inverse for (Z;+). So I get -4.

Precedence is a perfectly good way to specify what is meant. And that's all there is to it. There is no room for subjective opinions in Maths, all consistent conventions concerning well defined objects are trivially equivalent and once people agree on one there's no point in arguing or reinventing the wheel.

And I'm sorry, but that "2.5^2=2.25" has nothing to do with this convention (and writing it twice is two too many. )