8÷2(1+3)

[dm319]

(12-04-2023 12:30 AM)Thomas Klemm Wrote:  Do you agree or do you come up with another special rule out of thin air?

PEMDAS/BODMAS is not the rule book on the rules of algebra. You weren't taught it, and neither was I, so I guess we were taught a series of rules. To be fair, the acronym isn't even that good - it doesn't take into account multiply/divide and addition/subtraction being equal precedence, and it has no mention of the left-to-right rule.

So yes, I think there are plenty of special rules in maths, but they don't come from thin air. There's historical evidence to suggest that treating coefficients as a special case has been the case long before our calculators or programming languages. We were taught in school the rules for 'collecting like terms', and we were taught that x and x^2 are not like terms. The implication there is that the power takes precedence, and so we know it has precedence over the coefficient. I don't think that undermines coefficients being different to the multiply operator.

I agree though that there doesn't appear to be a formal documentation of these 'rules'.

(12-04-2023 12:30 AM)Thomas Klemm Wrote:  What are these?

Are you asking about inconsistencies or about Wolfram Alpha?

If you compare the result for:

8÷2b where b = 2
(8)

and:
8÷ab where a = 2 and b = 2
(2)

Anyway, I think it's an interesting subject, and it gets more curious the more I delve into it. I also find the different kinds of arguments about it interesting. Like whether we should care or not, whether we should use parens for everything, whether we should just accept the majority device way of doing it and move forward etc..