No worries

The “mysterious” they is HerelAm, the person I was replying to you ninny

The person who couldn't even manage to get 10-1+1 correct when doing addition first

Nope. It's still not a textbook. Sounds more like a higher education version of Wikipedia.

It is though. Here's a link to buy a printed copy: https://libretexts.org/bookstore/order?math-7309

You keep mentioning textbooks but haven't actually shown any that support you. I have. I'll trust the PhD teaching a university course on the subject over the nobody on the internet who just keeps saying "trust me bro" and then being condescending while also being embarrassingly wrong.

And because I can't help it, I'll also trust Wolfram over you: Examples of binary operation on A from A×A to A include addition (+), subtraction (-), multiplication (×) and division (÷). Here, you can buy a copy of this too: https://www.amazon.com/exec/obidos/ASIN/1420072218/weisstein-20

Says person who doesn't understand the difference between unary and binary.

Talking about yourself in the third person is weird. Even your nonsense about a silent "+" is really just leaving off the leading 0 in the equation 0+2. Because addition is a binary operator.

Apparently EVERYTHING is binary according to you (and your website).

Only the ones that operate on two inputs. Some examples of unary operators are factorial, absolute value, and trig functions. The laughing face when you make a fool of yourself isn't really as effective as you think it is.

But we're getting off topic again. I can't keep trying to explain the same thing to you, so I would say this has been fun, but it's been more like talking to an unusually obnoxious brick wall. Next time you want to engage with someone try being less of a prick, or at least less wrong. You're not nearly as smart as you seem to think you are.

It is though. Here’s a link to buy a printed copy:

BWAHAHAHAHAHAHA! They print it out when someone places an order!

You keep mentioning textbooks but haven’t actually shown any that support you. I have

No you haven't. You've shown 2 websites, both updated by random people.

I’ll trust the PhD teaching a university course on the subject

I already pointed out to you that they DON'T teach order of operations at University. It's taught in high school. Dude on page you referred to was teaching Set theory, not order of operations.

over the nobody on the internet

Don't know who you're referring to. I'm a high school Maths teacher, hence the dozens of textbooks on the topic.

Talking about yourself in the third person is weird

Proves I'm not weird then doesn't it.

Even your nonsense about a silent “+”

You call what's in textbooks nonsense? That explains a lot!

is really just leaving off the leading 0 in the equation 0+2

And yet the textbook says nothing of the kind. If I had 2+3, which is really +2+3 (see above textbook), do I, according to you, have to write 0+2+0+3? Enquiring minds want to know. And do I have to put another plus in front of the zero, as per the textbook, +0+2+0+3

Because addition is a binary operator

No it isn't

Only the ones that operate on two inputs.

Now you're getting it. Multiply and divide take 2 inputs, add and subtract take 1.

Some examples of unary operators are factorial, absolute value, and trig functions.

Actually none of those are operators. The first 2 are grouping symbols (like brackets, exponents, and vinculums), the last is a function (it was right there in the name). The only unary operators are plus and minus.

I can’t keep trying to explain the same thing to you

You very nearly got it that time though!

at least less wrong

Again, it's not me who's wrong.

They print it out when someone places an order!

Welcome to the 21st century. We have this thing called the internet so people can share information without killing trees. It's the resource material for a college course. That's like the definition of a text book without costing the students a month's rent.

random people.

One is a PhD teaching a college course on the subject, the other is Wolfram. Neither of those are "random people" and their credentials beat "claims to be a high school math teacher but had trouble counting to 2" pretty soundly.

I already pointed out to you that they DON'T teach order of operations at University. It's taught in high school. Dude on page you referred to was teaching Set theory, not order of operations.

This portion of the discussion wasn't about order of operations, it was about the number of inputs an operator (+, and - in this case) has. Try to keep up.

Don't know who you're referring to. I'm a high school Maths teacher, hence the dozens of textbooks on the topic.

Dear God if that's true I feel sorry for your students and embarrassed for whatever school is paying you. But this is the internet and with any luck that's a flat out lie. At least your repeated use of the plural maths means you're not anywhere near my kids. Also, has the line "I'm a high school math teacher" ever impressed anyone?

And yet the textbook says nothing of the kind. If I had 2+3, which is really +2+3..

Oh, I see the problem. We're back to reading comprehension. That section you highlighted specifically refers to when those symbols are being used as a "sign of the quality" of the number it's referring to, not when it's being used to indicate an operation like addition or subtraction. Hopefully that clears it up. This is ignoring the fact that a random screen shot could be anything. For all I know you wrote that yourself.

do I, according to you, have to write 0+2+0+3

No. You also don't need to write +2+3 because the first "+" isn't an operator. It's, as your own picture says, a sign of the quality of 2.

Now you're getting it. Multiply and divide take 2 inputs, add and subtract take 1.

I would love to know how you get to a sum or difference with only one input. Here, I'll try to spell it out using your own example so that even you can understand.

The inputs to 2 + 3 = 5 are 2 and 3. Let's count them together. 2 is the first, and 3 is the second. 1, 2. Two inputs for addition. Did you get it this time? Was that too fast? You can go back and read it again if you need to

Actually none of those are operators. The first 2 are grouping symbols

Fine, operation then. The fact that you think "!" is the same thing as brackets doesn't do anything to help your bona fides though. And I don't have the energy to write up a word doc and screen shot it since that's apparently what it takes for you to consider something valid.

Maybe you're just being weirdly pedantic about operator vs operation. Which would be a strange hill to die on since the original topic was operations.

You very nearly got it that time though!

If by "it" you mean through your thick skull, then you're more optimistic than I am. Keep laughing though, you just look dumber every time.

Again, it's not me who's wrong.

Again, according to literally everyone, it is. I could keep providing sources, but I still don't have the time to screen shot some random crap with no supporting evidence. And as much as I enjoy dunking on dipshits, I've got other things to do.

Welcome to the 21st century

Welcome to it's not a textbook (and it wasn't about order of operations anyway).

We have this thing called the internet so people can share information without killing trees

We also have this thing called textbooks, that schools order so that Maths classes don't have to be held in computer labs.

It’s the resource material for a college course

And the college doesn't teach order of operations.

That’s like the definition of a text book

by someone who can't back up their statements with actual textbooks.

One is a PhD teaching a college course on the subject

Yep, exactly what I said - a random person as far as order of operations is concerned, since he teaches Set Theory and not order of operations.

the other is Wolfram

Yeah, their programmers didn't know The Distributive Law either.

I’m willing to bet their credentials beat “claims to be a high school math teacher” pretty soundly

Happy to take that bet. Guarantee you neither of them has studied order of operations since they were in high school.

This portion of the discussion wasn’t about order of operations

Yes it is. I said that order of operations dictates that you have to solve binary operators before unary operators, then you started trying to argue about unary operators.

it was about the number of inputs an operator (+, and - in this case) has

Yep, the ones with more inputs, binary operators, have to be solved first.

Try to keep up

Says person who's forgotten why we were talking about it to begin with!

At least your repeated use of the plural maths means you’re not anywhere near my kids.

Well that outs yourself as living in a country which has fallen behind the rest of the world in Maths, where high school teachers don't even have to have Maths qualifications to teach Maths.

when those symbols are being used as a “sign of the quality” of the number it’s referring to

which is always. As usual, the comprehension issue is at your end.

not when it’s being used to indicate an operation like addition or subtraction

Yes it is

Hopefully that clears it up

That you still have comprehension issues? I knew that already

This is ignoring the fact that a random screen shot could be anything

The name of the book is in the top left. Not very observant either.

For all I know you wrote that yourself

You don't care how much you embarrass yourself do you, given the name of the book is in the top left and anyone can find and download it.

because the first “+” isn’t an operator

Yes it is!

It’s, as your own picture says, a sign of the quality of 2

and a sign of the quality of the 3 too. There are 2 of them, one for each Term, since it's a 1:1 relationship.

I would love to know how you get to a sum or difference with only one input.

You don't. Both need 2 Terms with signs. In this case +2 and +3.

2 is the first, and 3 is the second

Yep, corresponding to the 2 plus signs, +2 and +3. 1 unary operator, 1 Term, 2 of each.

Two inputs for addition

2 jumps on the number line, starting from 0, +2, then +3, ends up at +5 on the number line. This is how it's taught in elementary school.

Did you get it this time?

The real question is did you?

Was that too fast?

No, you just forgot one of the plus signs in your counting, the one we usually omit by convention if at the start of the expression (whereas we never omit a minus sign if it's at the start of the expression).

You can go back and read it again if you need to

I'm not the one who doesn't know how unary operators work. Try it again, this time not leaving out the first plus sign.

Fine, operation then

Nope, not an operation either.

The fact that you think “!” is the same thing as brackets

I see you don't know how grouping symbols work either.

Maybe you’re just being weirdly pedantic about operator vs operation

Grouping symbols are neither.

Which would be a strange hill to die on since the original topic was operations

You were the one who incorrectly brought grouping symbols into it, not me.

I could keep providing sources

You haven't provided any yet!

I still don’t have the time to screen shot some random crap with no supporting evidence

Glad you finally admitted you have no supporting evidence. Bye then!

Yes we are

Yes and no. You teach how to solve equations, but not the fundamentals (and if you do then kudos to you, as it's not a trivial accomplishment). Fundamentals, most of the time, are taught in universities. It's so much easier that way, but doesn't mean it's right. People call it math, which is fair enough, but it's not really math in a sense that you don't understand the underlying principles.

Yes there is!

Nope.

There's only commutation, association, distribution, and identity. It doesn't matter in which order you apply any of those properties, the result will stay correct.

2×2×(2-1)/2 = 2×(4-2)/2 = 1×(4-2) = 4-2 = 2

As you can see, I didn't follow any particular order and still got the correct result. Because no basic principle was broken.

Or I could also go

2×2×(2-1)/2 = 4×(2-1)/2 = 4×(1-0.5) = 4×0.5 = 2

Same result. Completely different order, yet still correct.

My response to the rest goes back to the aforementioned.

You teach how to solve equations, but not the fundamentals

Nope. We teach the fundamentals. Adults not remembering them doesn't mean they weren't taught. Just pick up a Maths textbook. It's all in there. Always has been.

Fundamentals, most of the time, are taught in universities

No they're not. They only teach order of operations from a remedial point of view. Most of them forget about The Distributive Law. I've seen multiple Professors be told by their students that they were wrong.

it’s not really math in a sense that you don’t understand the underlying principles

The Constructivist learners have no trouble at all understanding it.

Nope.

Yep!

There’s only commutation, association, distribution, and identity.

And many proofs of other rules, which you've decided to omit mentioning.

It doesn’t matter in which order you apply any of those properties, the result will stay correct

But the order you apply the operations does matter, hence the proven rules to be followed.

2×2×(2-2)/2

Notably you picked an example that has no addition, subtraction, or distribution in it. That's called cherry-picking.

Completely different order, yet still correct

Yep, because you cherry-picked a simple example where it doesn't matter. It's never going to matter when you only pick operations which have the same precedence.

My response to the rest goes back to the aforementioned

...cherry-picking.

We teach the fundamentals

Sure. They are, however, not the focus. At least that's not how I've been taught in school. You're not teaching kids how to prove the quadratic formula, do you? No, you teach them how to use it instead. The goal here is different.

They only teach order of operations.

Again, with the order of operations. It's not a thing. I've given you two examples that don't follow any.

The constructivist learners...

That's kinda random, but sure?

And many proofs of other rules...

They all derive from each other. Even those fundamental properties are. For example, commutation is used to prove identity.

But the order you apply operators does matter

2+2-2 = 4-2 = 2+0 = 0

2 operators, no order followed.

If we take your example

2+3×4 then it's not an order of operation that plays the role here. You have no property that would allow for (2+3)×4 to be equal 2+3×4

Look, 2+3×4 = 1+3×(2+2)+1 = 1+(6+6)+1 = 7+7 = 14

Is that not correct?

Notably you picked...

It literally has subtraction and distribution. I thought you taught math, no?

2-2 is 2 being, hear me out, subtracted from 2

Same with 2×(2-2), I can distribute the value so it becomes 4-4

No addition? Who cares, subtraction literally works the same, but in opposite direction. Same properties apply. Would you feel better if I wrote (2-2) as (1+1-2)? I think not.

Also, can you explain how is that cherry-picking? You only need one equation that is solvable out of order to prove order of operation not existing. One is conclusive enough. If I give you two or more, it doesn't add anything meaningful.

At least that’s not how I’ve been taught in school

If you had a bad teacher that doesn't mean everyone else had a bad teacher.

You’re not teaching kids how to prove the quadratic formula, do you?

We teach them how to do proofs, including several specific ones.

No, you teach them how to use it instead.

We teach them how to use everything, and how to do proofs as well. Your whole argument is just one big strawman.

Again, with the order of operations

Happens to be the topic of the post.

It’s not a thing

Yes it is!

I’ve given you two examples that don’t follow any

So you could not do the brackets first and still get the right answer? Nope!

2×2×(2-2)/2=0

2×2×2-2/2=7

That’s kinda random, but sure?

Not random at all, given you were talking about students understanding how Maths works.

2+3×4 then it’s not an order of operation that plays the role here

Yes it is! If I have 1 2-litre bottle of milk, and 4 3-litre bottles of milk, there's only 1 correct answer for how many litres of milk of have, and it ain't 20! Even elementary school kids know how to work it out just by counting up.

They all derive from each other

No they don't. The proof of order of operations has got nothing to do with any of the properties you mentioned.

For example, commutation is used to prove identity

And neither is used to prove the order of operations.

2 operators, no order followed

Again with a cherry-picked example that only includes operators of the same precedence.

You have no property that would allow for (2+3)×4 to be equal 2+3×4

And yet we have a proof of why 14 is the only correct answer to 2+3x4, why you have to do the multiplication first.

Is that not correct?

Of course it is. So what?

It literally has subtraction and distribution

No it didn't. It had Brackets (with subtraction inside) and Multiplication and Division.

I thought you taught math, no?

Yep, and I just pointed out that what you just said is wrong. 2-2(1+2) has Subtraction and Distribution.

2-2 is 2 being, hear me out, subtracted from 2

Which was done first because you had it inside Brackets, therefore not done in the Subtraction step in order of operations, but the Brackets step.

Also, can you explain how is that cherry-picking?

You already know - you know which operations to pick to make it look like there's no such thing as order of operations. If I tell you to look up at the sky at midnight and say "look - there's no such thing as the sun", that doesn't mean there's no such thing as the sun.