💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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22

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591

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2 yr. ago

I only just found the thread yesterday. There's only 1 "interpretation", and the only back and forth I've seen about interpretations is about implicit multiplication, which isn't a thing, at all - it's people conflating The Distributive Law and Terms dotnet.social/@SmartmanApps/110925761375035558

I Looked up doing factorials and n! = n(n – 1) is used interchangeably with n! = n*(n – 1)

Yeah, there's a problem with some lazy textbook authors, which I talked about here. A term is defined as ab=(axb), and yet many textbooks lazily write it as ab=axb, which is fine if that's the whole expression, but NOT fine if the expression is a/bc (a/(bxc) and a/bxc AREN'T the same thing!), and so we end up with people removing brackets prematurely and getting wrong answers. In other words, in your case, only n!=n(n – 1) and n!=(nx(n – 1)) can be used interchangeably.

The ÷ sign isn’t used by “Americans”, it’s used by small children

I don't know where you're from, but it's used universally in Australia - textbooks, calculators, all ages - and from what I've seen the U.K. too.

written like this (÷) means it’s a fraction?

No, that means it's a division. i.e. a÷b. To indicate it's a fraction it would need to be written as (a÷b). i.e. make it a single term. Terms are separated by operators and joined by grouping symbols (such as brackets or fraction bars).

put the whole 2(1+2) down there, there’s no reason for that.

There is - it's a single bracketed term, subject to The Distributive Law. i.e. the B in BEDMAS.

And they're all wrong dotnet.social/@SmartmanApps/111164851485070719

An e-calculator I'm guessing? (either that or Texas Instruments) Desmos USED TO interpret that correctly, but then they made a change with automatically turning division into fractions and broke it (because if you've specified division then it's not a fraction) dotnet.social/@SmartmanApps/111164851485070719

Just write it better.

6/(2(1+2))

If you really wanted extra brackets it'd be 6/(2)(1+2). Of course, since there's only 1 term in the first brackets they're redundant, hence 6/2(1+2) is the fully simplified form, and is the way it's written in Maths textbooks.

a/bc is equally as ambiguous as a/b*c

It's not ambiguous at all. By the definition of Terms - ab=(axb) - a/bc is 2 terms and a/bxc is 3 terms. If we were to write it in fraction form (to illustrate the difference), in the former c is in the denominator, but in the latter it's in the numerator, hence a different answer. dotnet.social/@SmartmanApps/110846452267056791

you seem to take the position that the operations are resolved from left to right... but I haven’t seen this defined in mathematics anywhere

It applies to operators, or more precisely division. When doing the divisions, you have to do them left-to-right, but other than that each of the operators can be done in any order. i.e. it doesn't matter what order you do the multiplications in, as long as you do them before the additions and subtractions. Unfortunately I've seen many people misremember left-to-right as an overarching rule, rather than only applying to division.

It's not ambiguous. People who say it is have usually forgotten The Distributive Law or Terms, or more commonly both!

Seems this whole thing is the pedestrian-math-nerd’s equivalent to the pedestrian-grammar-nerd’s arguments on the Oxford comma.

Not even remotely similar. Maths rules are fixed. The order of operations rules are at least 400 years old.

mathematical notation is just as flexible as any other facet of written human communication

No, it isn't. The book "A history of mathematical notation" is in itself more than 100 years old.

The meme refers to the problem of handling implicit multiplication

There's no such thing as implicit multiplication. dotnet.social/@SmartmanApps/110925761375035558

I don’t see the problem actually.

Everything between ()

You recreated the problem right there - ignored The Distributive Law. a(b+c)=(ab+ac). i.e. 2(1+2)=(2x1+2x2). After step 1 - solving brackets - all that's left is 6/6. dotnet.social/@SmartmanApps/110819283738912144

Excel and Google are both wrong. In fact, Microsoft excels 😂in this area, with Excel, the Windows calculator, and MathSolver all getting it wrong in different ways! dotnet.social/@SmartmanApps/111164851485070719

Starting a new comment thread (I gave up on reading all of them). I'm a high school Maths teacher/tutor. You can read my Mastodon thread about it at Order of operations thread index (I'm giving you the link to the thread index so you can just jump around whichever parts you want to read without having to read the whole thing). Includes Maths textbooks, historical references, proofs, memes, the works.

And for all the people quoting university people, this topic (order of operations) is not taught at university - it is taught in high school. Why would you listen to someone who doesn't teach the topic? (have you not wondered why they never quote Maths textbooks?)

#DontForgetDistribution #MathsIsNeverAmbiguous

Because as a high school Maths teacher as soon as I saw the assertion that it was ambiguous I knew the article was wrong. From there I scanned to see if there were any Maths textbooks at any point, and there wasn't. Just another wrong article.

Without parentheses around (2×3)

But there is parentheses around (2x3). a(b+c)=(ab+ac) - The Distributive Law. You can't remove them unless there is only 1 term left inside. You removed them when you still had 2 terms inside, 2x3.

6/2(1+2)=6/2(3)=6/(2*3)=6/6=1

OR

6/2(1+2)=6/(2+4)=6/6=1

2(1+2) is the same as (1+2)+(1+2)

You nearly had it. 2(1+2) is the same as (2x1+2x2). The Distributive Law - it's the reverse process to factorising.

The bot’s posts are

Yes, that was the point of my post - can now follow the blog directly.

Microsoft is not posting their content in a federated way

Well, they're using Wordpress, and Maho has activated the Wordpress ActivityPub plug-in to enable following it. Currently to comment on them you need to login (I guess with MS account?), so yes, would need it to be on official MS involvement for that change to happen, rather than something Maho has done in his spare time, because that would need an organisational change.

Yeah, people were saying that when dotnet.social launched as well, despite that not being an official MS server either.

It's not official but it is federated, demonstrably.