You’ve completely not understood that order of operations is an arbitrary convention. How did you decide to expand the definition of multiplication before evaluating the addition? Convention.
You can’t write 2 + 2 ÷ 2 like this, so how are you gonna decide whether to decide to divide or add first?
How are you gonna write 2 + 2 ÷ 2 with repeated addition?
The definition of Multiplication as being repeated addition
That doesn’t mean it has to be expanded first. You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2) and you are unable to tell me what mathematical law prohibits it.
If this were a universal law, reverse polish notation wouldn’t work as it does. In RPL, 2 2 + 3 × is 12 but 2 3 × 2 + is 8. If you had to expand multiplication first, how would it work? The same can be done with prefix notation, and the same can be done with “pre-school” order of operations.
Different programming languages have different orders of operations, and those languages work just fine.
Your argument amounts to saying that it makes the most sense to do multiplication before addition. Which is true, but that only gives you a convention, not a rule.
You’ve completely not understood that order of operations is an arbitrary convention. How did you decide to expand the definition of multiplication before evaluating the addition? Convention.
You can’t write 2 + 2 ÷ 2 like this, so how are you gonna decide whether to decide to divide or add first?
No, you’ve completely not understood that they are universal rules of Maths
The definition of Multiplication as being repeated addition
Yes you can
The rules of Maths, which says Division must be before Addition
How are you gonna write 2 + 2 ÷ 2 with repeated addition?
That doesn’t mean it has to be expanded first. You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2) and you are unable to tell me what mathematical law prohibits it.
If this were a universal law, reverse polish notation wouldn’t work as it does. In RPL, 2 2 + 3 × is 12 but 2 3 × 2 + is 8. If you had to expand multiplication first, how would it work? The same can be done with prefix notation, and the same can be done with “pre-school” order of operations.
Different programming languages have different orders of operations, and those languages work just fine.
Your argument amounts to saying that it makes the most sense to do multiplication before addition. Which is true, but that only gives you a convention, not a rule.