Unary minus precedence preference

[dm319]

And there are those that say we leave off a lot of operators and coefficients as they are assumed present. Arguably these operators are really always unary, was they only really relate to the number directly to the right:

2 - 3

is arguably:

+2 -3
or
-3 +2

With the number being left-associated with the operator, the '+' assumed and the order not really mattering.

I agree though that a negative number is a perfectly valid number, and it's hard to say that the number '3' can have the honour of being written 3², whereas the number '-3' does not have that honour and must sit in brackets. We also tend to put decimals in brackets too - i.e. I think 3.15² is usually written (3.15)². Even though on our RPN calculators we could easily square a perfectly valid number in our x register: -3.345x10³, I don't think any of us would expect to write that square without brackets.

But we can write a², even while a = -3.

I guess negative numbers and imaginary numbers aren't really 'real'. They are useful concepts to help our calculations. But we don't have negative mass, negative temperature, negative distances, negative apples in 'reality'.

In conclusion, unless you are a natural number, you can't expect to be a first class citizen in algebra!