💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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591

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2 yr. ago

implicit multiplication

There's no such thing as implicit multiplication

The parentheses step only covers expressions inside parentheses

No, it doesn't

16, is what you get by strictly following PEMDAS

except 1 is what you get from strictly following PEMDAS. If you got 16 then you missed one of more rules.

the rule is that multiplication and division have the same precedence, and you evaluate them from left-to-right

Go back and read your link again. You'll find they're obeying The Distributive Law. i.e. solve all brackets first, from inner-most out.

“implicit” multiplication

There's no such thing as implicit multiplication

follows the same rules you would have learnt in primary school

It's never that - that's how people are getting the wrong answer. In high school you get taught about The Distributive Law.

it’s (8 / 2) * 4

It's 8/2(2+2)=8/(4+4) or 8/2(2+2)=8/2(4)=8/(2x4)

Right answer but wrong reason. It's because distribution comes first

If you’re following ALL of the rules of PEMDAS then the answer is

...1. If you got 16 then there's one or more rules that you didn't obey.

I’m talking about the classic 4/2x. If x = 2, it is:

4/2x2 = 2x2 = 4

4/(2x2) = 4/4 = 1

It's the latter, as per the definition of Terms. There are references to this definition being used going back more than 100 years.

Wolfram solved this with going with the second if it is an X or another variable as it’s more intuitive

Yes, they do if it's 2x, but not if it's 2(2+2) - despite them mathematically being the same thing - leading to wrong answers to expressions such as the OP. In fact, that's true of every e-calculator I've ever seen, except for MathGPT (Desmos used to handle it correctly, but then they made a change to make it easier to enter fractions, and consequently broke evaluating divisions correctly).

how do you calculate 2(1+1)? It’s 4. It’s called implicit multiplication

No, it's not called implicit multiplication. It's distribution.

We could write this up as +2*(+1+(+1))

No, you can't. Adding that multiplication has broken it up into 2 terms. You either need to not add the multiply, or add another set of brackets if you do, to keep it as 1 term.

I can’t think of a situation where it’s incorrect

If a=2 and b=3, then...

1/axb=3/2

1/ab=(1/6)

If there is a letter or number or anything next to a bracket, it’s multiplication

No, it's distribution. Multiplication refers literally to multiplication signs, of which there aren't any in this expression.

2x is the same as 2*x

No, 2A is the same as (2xA). i.e. it's a single Term. 2xA is 2 Terms (multiplied).

If a=2 and b=3, then...

axb=2x3 (2 terms)

ab=6 (1 term)

This guy talks in hashtags.

Only in the first post in each thread, so that people following those hashtags will see the first post, and can then click on it if they want to see the rest of the thread. Also "this guy" is me. :-)

Grab a calculator, look at wolfram docs, ask a professor or teacher

I'm a Maths teacher with a calculator and many textbooks - I'm good. :-) Also, if you'd clicked on the thread you would've found textbook references, historical Maths documents, proofs, the works. :-)

8/2(2+2), let’s remove the confusion

8/2*(2+2), brackets

8/2*(4), mult & div, left -> right

4*(4), let go

2 mistakes here. Adding the multiplication sign in the 2nd step has broken up the term in the denominator, thus sending the (2+2) into the numerator, hence the wrong answer (and thus why we have a rule about Terms). Then you did division when there was still unsolved brackets left, thus violating order of operations rules.

it’s more like 8/(2x), but it’s just harder to read, so we don’t

But that's exactly what we do (but no extra brackets needed around 2x nor 2(2+2) - each is a single term).

you could argue that it should be handled like the scenario with the x

Which is what the rules of Maths tells us to do - treat a single term as a single term. :-)

there are no rules of this

Yeah, there is. :-)

you use fractions instead of inline division

No, never. A fraction is a single term (grouped by a fraction bar) but division is 2 terms (separated by the division operator). Again it's the definition of Terms.

And by all means, correct me if I’m wrong

Have done, and appreciate the proper conversation (as opposed to those who call me names for simply pointing out the actual rules of Maths).

link something that isn’t an unreadable

No problem. I t doesn't go into as much detail as the Mastodon thread though, but it's a shorter read (overall - with the Mastodon thread I can just link to specific parts though, which makes it handier to use for specific points), just covering the main issues.

as long as we are civilised

Thanks, appreciated.

Thanks for the correction, you are right

The point is the correction, not who made it. Almost every e-calculator is wrong, so people need to stop trusting them. They're no more accurate than GPT. Use a proper calculator.

Knowing the rules of Maths means someone might be drunk? Interesting conclusion.

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

Wolfram-Alpha’s equation parser is wrong

the rules of math are not set in stone

The rules around order of operations are!

if your notation is ambiguous or unclear to your audience try to fix it

Nothing ambiguous in this expression.

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.

They do care. The issue is everyone argues about it without even asking Maths teachers about it to being with! I guarantee (I've seen it myself) literally every blog you read which says this is "ambiguous", without exception they never mention Maths textbooks or Maths teachers (because then they wouldn't be able to bombastically declare "This is ambiguous!").

write ambigous terms like this

It's not ambiguous

all the people in the comments who weren’t educated properly on what conventions are

Everyone was taught the rules of Maths - it's just a matter of who remembers them or not.

rules nobody can even agree on!

All the Maths textbooks agree

Thanks for the effort!

You're welcome.