Multiplication precedes Negation

[Atran]

Hi,

Example 1.2.1. We have −3 × 4 − 5 + (−3) = −(3 × 4) − 5 + (−3) = −12 − 5 − 3 = −20. Note that we have recognized that 3 × 4 takes precedence over the − signs.

Does the author mean that −3 × 4 = 0 − 3 × 4 = −(3 × 4) or else?

I consider the minus-sign to be a unary operator, which is preceded by multiplication and division. Am I thinking right?

 

[arildno]

It won't matter if you, with the unary operator of negation choose to regard -3*4 as (-3)*4 or as -(3*4). That is, the order of the unary operator and multiplication need not be formally agreed upon.

 

[verty]

I think it is safe to assume that a unary operator without parentheses is meant to bind more tightly than any operator near it. So unary negation you may assume applies to the term directly in front of it.

 

[Office_Shredder]

When he says precedence over the minus signs he's referring to doing the 3*4 calculation before the -5 +(-3) calculation. As arildno says it doesn't matter whether you calculate (-3)*4 or -(3*4) as those are the same thing

 

[arildno]

I think it is safe to assume that a unary operator without parentheses is meant to bind more tightly than any operator near it. So unary negation you may assume applies to the term directly in front of it.

That is my gut feeling as well, but since the unary negation -x always can be replaced with the binary operator (-1)*x, it cannot possibly matter multiplicationwise whatever you choose to read it as.

 

[D H]

I consider the minus-sign to be a unary operator, which is preceded by multiplication and division. Am I thinking right?

There is no consensus on the precedence of the unary + and - versus multiplication/division. Some place it higher (but almost always lower than exponentiation), others lower (and at the same level as addition and subtraction). It doesn't matter for the kinds of numbers with which you are accustomed. The end result will be the same regardless of whether you treat unary minus as being higher or lower than multiplication.

 

[arildno]

The really fun thing about the negation, though, is how it can jump over a bundle of factors to find one to its liking, even take a step down to the denominator if it wants to, and then rush back again, or stay put. It doesn't matter.

(It should not push its luck down a continued fraction, though...)

 

[Atran]

Thank you for your response. I'm thinking to stick with the precedence level above that of multiplication.

Instead of starting a new thread: I consider a value to be a computed or assigned number or quantity. What's the difference between number and quantity? What exactly are number, quantity and value?

Thanks for help.