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some typos and a modification for association of + and *

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Fang Liu 2025-04-16 15:18:55 +08:00
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quarto/precalc/calculator.qmd
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@ -244,7 +244,7 @@ With the Google Calculator, typing `1 + 2 x 3 =` will give the value $7$, but *i
In `Julia`, the entire expression is typed in before being evaluated, so the usual conventions of mathematics related to the order of operations may be used. These are colloquially summarized by the acronym [PEMDAS](http://en.wikipedia.org/wiki/Order_of_operations).
> **PEMDAS**. This acronym stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. The order indicates which operation has higher precedence, or should happen first. This isn't exactly the case, as "M" and "D" have the same precedence, as do "A" and "S". In the case of two operations with equal precedence, *associativity* is used to decide which to do. For the operations `-`, `/` the associativity is left to right, as in the left one is done first, then the right. However, `^` has right associativity, so `4^3^2` is `4^(3^2)` and not `(4^3)^2` (Be warned that some calculators - and spread sheets, such as Excel - will treat this expression with left associativity.) But, `+` and `*` don't have associativity, so `1+2+3` can be `(1+2)+3` or `1+(2+3)`.
> **PEMDAS**. This acronym stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. The order indicates which operation has higher precedence, or should happen first. This isn't exactly the case, as "M" and "D" have the same precedence, as do "A" and "S". In the case of two operations with equal precedence, *associativity* is used to decide which to do. For the operations `-`, `/` the associativity is left to right, as in the left one is done first, then the right. However, `^` has right associativity, so `4^3^2` is `4^(3^2)` and not `(4^3)^2` (Be warned that some calculators - and spread sheets, such as Excel - will treat this expression with left associativity). But, `+` and `*` don't have associativity, so `1+2+3` can be `(1+2)+3` or `1+(2+3)`.