💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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2 yr. ago

Division and multiplication are equal in the order of operations

I didn't say they weren't. I said...

Doing division before brackets goes against the order of operations rules

You did 8/2x4, which is the same as (8/2)(2+2), which isn't the same as 8/2(2+2)=8/2(4)=8/(2x4).

Please learn some math

I'm a Maths teacher - how about you?

Quoting yourself as a source

I wasn't. I quoted Maths textbooks, and if you read further you'll find I also quoted historical Maths documents, as well as showed some proofs.

I didn't say the distributive property, I said The Distributive Law. The Distributive Law isn't ax(b+c)=ab+ac (2 terms), it's a(b+c)=(ab+ac) (1 term), but inaccuracies are to be expected, given that's a wikipedia article and not a Maths textbook.

I did read the answers, try doing that yourself

I see people explaining how it's not ambiguous. Other people continuing to insist it is ambiguous doesn't mean it is.

let me take this seriously for a second

You need to take it seriously for longer than that.

implies that they are provably distinct functions

No, I'm explicitly stating they are.

we can use the usual set-theoretic definition

This is literally Year 7 Maths - I don't know why some people want to resort to set theory.

Can you give me such a pair of numbers?

But that's the problem with your example - you only tried it with 2 numbers. Now throw in another division, like in that other Year 7 topic, dividing by fractions.

1÷1÷2=½ (must be done left to right)

1÷½=2

In other words 1÷½=1÷(1÷2) but not 1÷1÷2. i.e. ½=(1÷2) not 1÷2. Terms are separated by operators (division in this case) and joined by grouping symbols (brackets, fraction bar), and you can't remove brackets unless there is only 1 term left inside, so if you have (1÷2), you can't remove the brackets yet if there's still some of the expression it's in left to be solved (or if it's the last set of brackets left to be solved, then you could change it to ½, because ½=(1÷2)).

Therefore, as I said, division and fractions aren't the same thing.

apologise for the smugness

Apology accepted.

The y(n+1) is same as yn + y

No, it's the same as (yn+y). You can't remove brackets unless there is only 1 term left inside.

if you removed the “6÷” part. It’s

...The Distributive Law.

Semantically, yes they are

No, they're not. Terms are separated by operators (division) and joined by grouping operators (fraction bar).

That just states that a*(b + c) = ab + ac

No, The Distributive Law states that a(b+c)=(ab+ac), and that you must expand before you simplify.

For some simple exanples,

Examples by people who simply don't remember all the rules of Maths. Did you read the answers?

No, 8 / 2 happens before 2 * 4

That's (2x4). Doing division before brackets goes against the order of operations rules.

What order you do your exponents in is another ambiguity though

No it isn't - top down.

Brackets are ALWAYS first.

neither defines wether implied multiplication is a multiply/divide operation or a bracketed operation

The Distributive Law says it's a bracketed operation. To be precise "expand and simplify". i.e. a(b+c)=(ab+ac).

1/2x and expect you to know which one I meant with no additional context or brackets

By the definition of Terms, ab=(axb), so you most certainly can write that (and Maths textbooks do write that).

Sorry but both my phone calculator and TI-84 calculate 1/2X

...and they're both wrong, because they are disobeying the order of operations rules. Almost all e-calculators are wrong, whereas almost all physical calculators do it correctly (the notable exception being Texas Instruments).

You are saying that an implied operation has higher priority than one which I am defining as part of the equation with an operator? Bogus. I don’t buy it. Seriously when was this decided?

The rules of Terms and The Distributive Law, somewhere between 100-400 years ago, as per Maths textbooks of any age. Operators separate terms.

I am no mathematics expert... never heard this “rule” before.

I'm a High School Maths teacher/tutor, and have taught it many times.

never a division in sight

There is, especially if you're dividing by a fraction! Division and fractions aren't the same thing.

if you see two divisions anywhere in his work he’s using fractional notation

Not if it actually is a division and not a fraction. There's no problem with having multiple divisions in a single expression.

denotes it with “/” likely to make sure you treat it as a fraction

It's not the slash which makes it a fraction - in fact that is interpreted as division - but the fact that there is no space between the 2 and the square root - that makes it a single term (therefore we are dividing by the whole term). Terms are separated by operators (2 and the square root NOT separated by anything) and joined by grouping symbols (brackets, fraction bars).

used juxtaposition for multiplication bound more tightly than division

It's called Terms - Terms are separated by operators and joined by grouping symbols. i.e. ab=(axb).

The real answer is that anyone who deals with math a lot would never write it this way

Yes, they would - it's the standard way to write a factorised term.

but use fractions instead

Fractions and division aren't the same thing.

It’s not a law of maths in the way that 1+1=2 is a law

Yes it is, literally! The Distributive Law, and Terms. Also 1+1=2 isn't a Law, but a definition.

So 1/2x is universally interpreted as 1/(2x)

Correct, Terms - ab=(axb).

people doing academic research in maths, not primary school teachers

Don't ask either - this is actually taught in Year 7.

if they realise it’s over a question like this they’ll probably end up saying “it’s deliberately ambiguous in an attempt to start arguments”

The university people, who've forgotten the rules of Maths, certainly say that, but I doubt Primary School teachers would say that - they teach the first stage of order of operations, without coefficients, then high school teachers teach how to do brackets with coefficients (The Distributive Law).

Not sure what exactly this convention is called

It's 2 actual rules of Maths - Terms and The Distributive Law.

never ambiguous

Correct.

there is no right or wrong

Yes there is - obeying the rules is right, disobeying the rules is wrong.

Depends on the system you use

There are no other systems - only people who are following the actual rules of Maths and those who aren't. And yes, 1 is the correct answer

Casio calculators do implicit multiplication first

Actually they follow the actual rules of Maths - Terms and The Distributive Law.