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

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magidin@math.berkeley.edu

Posts: 11,155
Registered: 12/4/04
Re: Reason for operator precedence
Posted: Mar 14, 2006 10:37 AM
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In article <4416a498$1_4@news.peopletelecom.com.au>,
Tony <ignorethis@nowhere.com> wrote:
>Hi all.
>
>Hope this isn't a silly question.
>
>I was wondering what the reason is for having multiple levels of operator
>precedence?


So that polynomials and rational functions can be written
easily. That's essentially the main reason.

>Phrased another way, why is it that we don't just evaluate everything from
>left to right?


>Having multiple levels of precedence obviously adds complexity, so I assume
>there must be some payback. However, I don't see what it is.


So, by "evaluting left to right", I assume that you mean that
something like

2 + 3 * 5

would evaluate to 25, since 2 plus 3 is five, and then multiplying
that by 5 yields 25.

A general quadratic polynomial, using standard operator percedence, is
written as:

ax^2 + bx + c

And it can be written in other orders easily if you want:

c + bx + ax^2

bx + c + ax^2

etc.

How would you have to write it if you simply evaluated left to right?
The smallest number of parenthesis I can come up with is:

axx + (bx + c)

which may obscure the degree. If you want to put in the square, you
would need to do something like

bx + c + (a(x^2)).

Higher degree polynomials would be even harder.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@math.berkeley.edu




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