Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Reason for operator precedence
Replies: 15   Last Post: Mar 15, 2006 8:56 AM

 Messages: [ Previous | Next ]
 matt271829-news@yahoo.co.uk Posts: 2,136 Registered: 1/25/05
Re: Reason for operator precedence
Posted: Mar 14, 2006 8:53 AM

Dik T. Winter wrote:
> In article <1142342196.542632.294210@i39g2000cwa.googlegroups.com> matt271829-news@yahoo.co.uk writes:
> > Tony wrote:
> ...
> > > I was wondering what the reason is for having multiple levels of operator
> > > precedence?

> ...
> > As far as addition/subtraction vs multiplication/division is concerned,
> > one reason is to ensure that the distributive property of
> > multiplication works sensibly. For example, we want 3*(4 + 6) = 3*4 +
> > 3*6 = 3*(6 + 4) = 3*6 + 3*4.
> >
> > And for exponentiation we want, for example, 3*3^2 = 3^3, not (3*3)^2

>
> That is not the reason. You could just as well have left to right
> operation when you use sufficiently many parenthesis in the euqations.
> E.g. 3*(4 + 6) = (3*4) + (3*6).

Well, obviously any precedence can be enforced with parentheses. I
meant make it work *without* the need for parentheses, just as in your
example below.

>
> But try to write the polynomial x^7 + 2x^6 - 3x^5 + 2x^4 +7x^3 - 3x^2 - 5x + 8
> without assuming precedence. It is to avoid large numbers of parenthesis.