Actually, it is. Written by a PhD and used in a college course. It just happens to be distributed for free because Canada is cool like that.

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May want to work on your own reading comprehension.

It's not me who doesn't understand the difference.

The facts disagree.

You can keep saying defined all you want, it doesn't change the underlying issue that it's defined by man. In the absence of all your books (which you clearly don't understand anyway based on our discussion of unary vs binary) order of operations only exists because we all agree to it.

What proof do you have that using a left to right rule is universally true?

From my understanding It’s an agreed convention that is followed

Read what I wrote again. I already said that left to right is a convention, and that Left Associativity is a rule. As long as you obey the rule - Left Associativity - you can follow whatever convention you want (but we teach students to do left to right, because they often make mistakes with signs when they try doing it in a different order, as have several people in this thread).

that implies we could have a right to left rule

You can have a right to left convention if the rule is Right Associativity.

It’s also true that not all cultures right in the same way

Yeah, I don't know how they do Maths - if they do it the same as us or if they just flip everything back-to-front (or top to bottom - I guess they would). In either case all the rules on top stay the same once the direction is established (like I guess exponents would now be to the top left not the top right? but in any case the evaluation of an exponent would stay the same).

But here is an interesting quote from Florian Cajori in his book a history of mathematical notations

Yeah, he's referring to the conventions - such as left to right - not the rule of Left Associativity, which all the conventions must obey. For a while Lennes was doing something different - because he didn't understand Terms - and was disobeying Left Associativity, (which meant his rules were at odds with everyone else), but his rule died out within a generation of his death,. Absolutely all textbooks now obey Left Associativity, same as before Lennes came along.

Lastly here is an article that also highlights the issue

Not really. Just another person who has forgotten the rules.

"as it happens, the accepted convention says the second one is correct"

No it isn't. The Distributive Law says the first is correct (amongst 4 other rules of Maths which also say the answer is only 1). The second way they did it disobeys The Distributive Law (and 4 other rules) and is absolutely wrong.

You're literally arguing nothing right now. THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY. It doesn't matter when they were invented. Obviously it's never been written like that. They are the one arguing it SHOULD BE. I said that would be stupid vs following the left to right convention already established. You're getting caught up in the semantics of the wording.

What you inferred: they're saying brackets were always around and we chose left to right to avoid bracket mess.

What I was actually saying: we chose and continue to choose to keep using the left to right convention over brackets everywhere because it would be unnecessary and make things more cluttered.

And yes, that IS a position mathematicians COULD have chosen once brackets WERE invented. They could have decided we should use them in every equation for absolute clarity of order. Saying we should not do that based on tradition alone is a bad reason.

The "always been the case" argument could justify any legacy system. We don't still use Roman numerals for arithmetic just because they were traditional. Things DO change.

Ancient Greeks and Romans strongly resisted zero as a concept, viewing it as philosophically problematic. Negative numbers were even more controversial with many mathematicians into the Renaissance calling them "fictitious" or "absurd numbers." It took centuries for these to become accepted as legitimate mathematical objects.

Before Robert Recorde introduced "=" in 1557, mathematicians wrote out "is equal to" in words. Even after its introduction, many resisted it for decades, preferring verbal descriptions or other symbols.

I could go on but if you're going to argue why something shouldn't be the case, you should argue more than "it's tradition" or "we've done fine without it so far". Because they did fine with many things in mathematics until they decided they needed to change or expand it.

Actually, it is. Written by a PhD and used in a college course.

Yeah there's an issue with them having forgotten the basic rules, since they don't actually teach them (except in a remedial way). Why do you think I keep trying to bring you back to actual Maths textbooks?

May want to work on your own reading comprehension.

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

The facts disagree

With you, yes.

it doesn’t change the underlying issue that it’s defined by man.

The notation is, the rules aren't.

In the absence of all your books (which you clearly don’t understand anyway based on our discussion of unary vs binary)

Says person who doesn't understand the difference between unary and binary. Apparently EVERYTHING is binary according to you (and your website).

order of operations only exists because we all agree to it

It exists whether we agree with it or not. Don't obey it, get wrong answers.

Thank you very much for the detailed response! Very informative and interesting.

THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY

Who's this mysterious "THEY" you are referring to, because I can assure you that the history of Maths tells you that is wrong. e.g. look in Cajori and you'll find the order of operations rules are at least 2 centuries older than the use of Brackets in Maths.,

It doesn’t matter when they were invented

The rules haven't changed since then.

They are the one arguing it SHOULD BE

...and watch Physicists and Mathematicians promptly run out of room on blackboards if they did.

You’re getting caught up in the semantics of the wording

No, you're making up things that never happened.

they’re saying brackets were always around and we chose left to right to avoid bracket mess

and that's wrong. Left to right was around before Brackets were.

we chose and continue to choose to keep using the left to right convention over brackets everywhere

and you're wrong, because that choice was made before we'd even started using Brackets in Maths, by at least a couple of centuries.

it would be unnecessary and make things more cluttered

They've always been un-necessary, unless you want to deviate from the normal order of operations.

They could have decided we should use them in every equation for absolute clarity of order

But they didn't, because we already had clarity over order, and had done for several centuries.

Saying we should not do that based on tradition alone is a bad reason.

Got nothing to do with tradition. Got no idea where you got that idea from.

Things DO change.

The order of operations rules don't, and the last change to the notation was in the 19th Century.

I could go on

and you'd still be wrong. You're heading off into completely unrelated topics now.

you should argue more than “it’s tradition” or “we’ve done fine without it so far”

I never said either of those things.

Because they did fine with many things in mathematics until they decided they needed to change or expand it

And they changed the meaning of the Division symbol sometime in the 19th Century or earlier, and everything has been settled for centuries now.

The "mysterious" they is HerelAm, the person I was replying to you ninny.

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.

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!