That’s an after the fact justification
You got some sources with dates in them to show it was "after", and not, you know, before?
Please see this section of Wikipedia on the order of operations
That section is about multiplication, and there isn't any multiplication in this expression.
The “math” itself might not be ambiguous, but how we write it down absolutely can be
Not in this case it isn't. It has been written in a way which obeys all the rules of Maths.
This is why you don’t see actual mathematicians arguing over which one of these calculators is correct
But I do! I see University lecturers - who have forgotten their high school Maths rules (which is where this topic is taught) - arguing about it.
it is not either calculator being wrong
Yes, it is. The app written by the programmer is ignoring The Distributive Law (most likely because the programmer has forgotten it and not bothered to check his Maths is correct first).
US - PEMDAS vs UK - BODMAS
Those aren't the rules. They are mnemonics to help you remember the rules
notice division and multiplication swapped places
Yes, that's right, because they have equal precedence and it literally doesn't matter which way around you do them.
you can’t actually do all of the multiplication and division at one time
Yes, you can!
Some are taught to simply work left to right
Yes, that's because that's the easy way to obey the actual rule of Left associativity.
we are all taught to use parentheses correctly to eliminate ambiguity
Correct! So 2(2+2) unambiguously has to be done before the division.
go past past high school and this isn’t remotely true
But this is a high school Maths question, so "past high school" isn't relevant here.
Mathematicians know wolfram is wrong
Woo hoo! I hadn't heard of anyone else pointing this out (rather, I'm always on the receiving end of "But Wolfram says..."), so thanks for this comment! :-) Now I know I'm not alone in knowing that Wolfram is wrong.
like claiming the world isn’t definitely round because some people argue its flat
OMG, I've run into so many people like that. They seem to believe (via saying "look, this blog says it's ambiguous too") that 2 wrongs make a right. No, you're both just wrong! Wolfram, Google, ChatGPT(!), the guy who should mind his own business, are all wrong.
Sometimes people are wrong
Yes, they are... and unfortunately a whole bunch of the time they're unwilling to face it and/or admit it, even when faced with Maths textbooks which clearly show what they said is wrong.
they don’t typically write division inline like that
Yes we do.
But if you want to argue that Wolfram-Alpha’s equation parser is wrong go ahead
math is literally the only subject that has rules set in stone
Indeed, it does.
This example is specifically made to cause confusion.
No, it isn't. It simply tests who has remembered all the rules of Maths and who hasn't.
Division has the same priority as multiplication
And there's no multiplication here - only brackets and division (and addition within the brackets).
A fraction could be writen up as (x)/(y) not x/y
Neither of those. A fraction could only be written inline as (x/y) - both of the things you wrote are 2 terms, not one. i.e. brackets needed to make them 1 term.
The fact that some people argue that you do () first and then do what’s outside it means that
...they know all the relevant rules of Maths
look up the facts for yourself
You can find them here
your comment is just as incorrect as everyone who said the answer is 1
and 1 is 100% correct.
well they don’t agree on 0^0
Yes they do - it's 1 (it's the 5th index law). You might be thinking of 0/0, which depends on the context (you need to look at limits).
you could easily make this more straightforward by putting parentheses around 8÷2
But that would be a different expression with a different answer (16 rather than 1). This is the mistake made by the programmer of the e-calc - treats it as though there's extra brackets there when there isn't.
a(b) is a×b
a(b) is (a×b) - you can't remove brackets unless there is only 1 term left inside.
8/(2x4)=8/8=1
They were right but for the wrong reason
As are you. There is no such thing as implicit multiplication - the actual relevant rules are Terms and The Distributive Law.
explicitly ambiguous
#MathsIsNeverAmbiguous #DontForgetDistribution
This has been resolved by updating to VS 17.8.7 or 17.9
Are you talking about the lack of indentation? I don't know why it does that. I tried using with the same result. I'd fix it if I knew how!
Well, I just had an issue then here with and eventually found backslash worked - I'll give that a go (not sure if I already tried it before).
Ok, that's a start.
Exactly! So when a=2 then 4÷a=2, and 4a=8, which isn't the same thing. Welcome to why 2a and 2xa (and therefore also 2.a) aren't the same thing.
But that is incorrect. A dot is used for multiplication. i.e. it separates terms. If you use a . for 2.a, then you are writing the same thing as 2xa, not the same thing as 2a.
Well, that's fine enough if you keep it to yourself, but don't use it in anything anyone else is going to read, or you're going to run into the issues I just pointed out