Re: Reason for operator precedence

In article <1142342196.542632.294210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> matt271829-news@xxxxxxxxxxx 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).

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.
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