(-) precedence

[David Hayden]

The problem here is that we're using the same "-" character for three different, albeit related, concepts:

• Subtraction: a - b
• Unary negation: -x
• Negative numbers: -2.3
  

It's easy enough to say that unary negation has lower precedence than powers, and thus -x² is -(x²), but we have an understandable aversion to saying that to square the number -2.3, you must put parentheses around it (-2.3)²). It's the same aversion to saying that 2.3² should be 2+(.3²) because the powers should have higher precedence than the radix mark. The radix mark is part of the number, and since numbers atomic, their expression naturally should not require parentheses.

If only we used a different symbol to signify that a number is negative, all this confusion would disappear. Unfortunately, we're stuck with the notation that we have.