Yes, it is

No it isn't.

The division of a by b in the set of real numbers and the set of rational numbers (which are, de facto, the default sets used in most professions) is defined as the multiplication of a by the multiplicative inverse of b

No it isn't. The Quotient is defined as the number obtained when you divide the Dividend by the Divisor. Here it is straight out of Euler...

Alternative definitions are also based on a multiplication

Emphasis on "alternative", not actual.

I've seen many of his videos and haven't noticed any obvious errors. Could you please link to the specific video(s) that you are referencing in regards to errors he has made, especially those related to the distributive law and what you reference to as "1917," as well as any explanation as to what is incorrect/misleading/lying?

No it isn't.

Yes, it is.

No it isn't. The Quotient is defined as the number obtained when you divide the Dividend by the Divisor. Here it is straight out of Euler...

I'm defining the division operation, not the quotient. Yes, the quotient is obtained by dividing... Now define dividing.

Emphasis on "alternative", not actual.

The actual is the one I gave. I did not give the alternative definitions. That's why I said they are also defined based on a multiplication, implying the non-alternative one (understand, the actual one) was the one I gave.

Feel free to send your entire Euler document rather than screenshotting the one part you thought makes you right.

Note, by the way, that Euler isn't the only mathematician who contributed to the modern definitions in algebra and arithmetics.

I’m defining the division operation, not the quotient

Yep, the quotient is the result of Division. It's right there in the definition in Euler. Dividend / Divisor = Quotient <= no reference to multiplication anywhere

Yes, the quotient is obtained by dividing… Now define dividing.

You not able to read the direct quote from Euler defining Division? Doesn't mention Multiplication at all.

The actual is the one I gave

No, you gave an alternative (and also you gave no citation for it anyway - just something you made up by the look of it). The actual definition is in Euler.

That’s why I said they are also defined based on a multiplication

Again, emphasis on "alternative", not actual.

implying the non-alternative one (understand, the actual one) was the one I gave

The one you gave bears no resemblance at all to what is in Euler, nor was given with a citation.

Feel free to send your entire Euler document rather than screenshotting the one part

The name of the PDF is in the top-left. Not too observant I see

you thought makes you right

That's the one and only actual definition of Division. Not sure what you think is in the rest of the book, but he doesn't spend the whole time talking about Division, but feel free to go ahead and download the whole thing and read it from cover to cover to be sure!

Note, by the way, that Euler isn’t the only mathematician who contributed to the modern definitions in algebra and arithmetics.

And none of the definitions you have given have come from a Mathematician. Saying "most professions", and the lack of a citation, was a dead giveaway!

But +, -, *, and / are all binary operators?

As far as I know, the only reason multiplication and division come first is that we've all agreed to it. But it can't be derived in a vacuum as that other dude contends it should be.

Can you explain how that is? Like with an example?

Math is exactly like English. It's a language. It's an abstraction to describe something. Ambiguity exists in math and in English. It impacts the validity of a statement. Hell the word statement is used in math and English for a reason.

But +, -, *, and / are all binary operators?

No, only multiply and divide are. 2+3 is really +2+3, but we don't write the first plus usually (on the other hand we do always write the minus if it starts with one).

As far as I know, the only reason multiplication and division come first is that we’ve all agreed to it.

No, they come first because you get wrong answers if you don't do them first. e.g. 2+3x4=14, not 20. All the rules of Maths exist to make sure you get correct answers. Multiplication is defined as repeated addition - 3x4=3+3+3+3 - hence wrong answers if you do the addition first (just changed the multiplicand, and hence the answer). Ditto for exponents, which are defined as repeated multiplication, a^2=(axa). Order of operations is the process of reducing everything down to adds and subtracts on a number line. 3^2=3x3=3+3+3

Can you explain how that is? Like with an example?

I'm not sure what you're asking about. Explain what with an example?

Math is exactly like English. It’s a language

No it isn't. It's a tool for calculating things, with syntax rules. We even have rules around how to say it when speaking.

It’s an abstraction to describe something

And that something is the Laws of the Universe. 1+1=2, F=ma, etc.

Hell the word statement is used in math and English for a reason

You won't find the word "statement" used in Maths textbooks. I'm guessing you're referring to Expressions.

Those rules are based on axioms which are used to create statements which are used within proofs. As far as I know statements are pretty common and are a foundational part of all math.

Defining math as a language though is also going to be pointless here. It's not really a yes or no thing. I'll say it is a language but sure it's arguable.

And again laws are created using statements. I have plenty of textbooks that contain "statements"

I’ve seen many of his videos and haven’t noticed any obvious errors.

He makes mistakes every time there's Brackets with a Coefficient. He always does a(b)=axb, instead of a(b)=(axb), hence wrong every time it follows a division.

what you reference to as “1917,”

No, he calls it that, though sometimes he also tries to claim it's an article (it isn't - it was a letter) - he never refers to Lennes by name. He also ignores what it actually says, and in fact disobeys it (the rule proposed by Lennes was to do all multiplication first, and yet he proceeds to do the division first, hence wrong answer, even though he just claimed that 1917 is the current rule).

Here's a thread about Lennes' 1917 letter, including a link to an archived copy of it.

Here's where Presh Talwalker lied about 1917

Here's a thread about The Distributive Law

Here's where Presh Talwalker disobeyed The Distributive Law (one of many times) (he does 2x3 instead of (2x3), hence gets the wrong answer). What he says is the "historical" rule in "some" textbooks, is still the rule and is used in all textbooks, he just never looked in any!

Note that, as far as I can tell, he doesn't even have any Maths qualifications. He keeps saying "I studied Maths at Harvard", and yet I can find no evidence whatsoever of what qualifications he has - I suspect he dropped out, hence why he keeps saying "I studied...". In one video he even claimed his answer was right because Google said so. I'm not kidding! He's a snake oil salesman, making money from spreading disinformation on Youtube - avoid at all cost. There are many freely-available Maths textbooks on the Internet Archive if you want to find proof of the truth (some of which have been quoted in the aforementioned thread).

Those rules are based on axioms

Nope! The order of operations rules come from the proof of the definitions in the first place. 3x4=3+3+3+3 by definition, therefore if you don't do the multiplication first in 2+3x4 you get a wrong answer (having changed the multiplicand).

As far as I know statements are pretty common

And yet you've not been able to quote a Maths textbook using that word.

are a foundational part of all math

Expressions are.

It’s not really a yes or no thing

It's really a no thing.

And again laws are created using statements

Not the Laws of Maths. e.g. The Distributive Law is expressed with the identity a(b+c)=(ab+ac). An identity is a special type of equation. We have...

Numerals

Pronumerals

Expressions

Equations (or Formula)

Identities

No statements. Everything is precisely defined in Maths, everything has one meaning only.

Order of operations is not a hard rule. It is a convention. It's something agreed upon but is it not something that is universally true.

Solve for X

X^2=4

Typical examples of binary operations are the addition (
+
{\displaystyle +}) and multiplication (
×
{\displaystyle \times }) of numbers and matrices

Very confidently getting basic facts wrong doesn't inspire confidence in the rest of your comments.

Your example still doesn't give a reason why 2 + 3 * 4 is 2 + 3 + 3 + 3 +3 instead of 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 other than that we all agree to it.

Order of operations is not a hard rule

Yes it is.

It is a convention.

Left to right is a convention. Left Associativity is a hard rule. Left to right is a convention which obeys the rule of Left Associativity.

It’s something agreed upon

It's something that is a natural consequence of the definitions of the operators in the first place. As soon as Multiplication was defined in terms of Addition, that guaranteed we would always have to do Multiplication before Addition to get right answers.

is it not something that is universally true

Yes it is! All of Maths is universally true!

Solve for X X^2=4

You know that's no longer an order of operations problem, right?

Very confidently getting basic facts wrong doesn’t inspire confidence in the rest of your comments.

...says person quoting Wikipedia and NOT a Maths textbook!

Your example still doesn’t give a reason why 2 + 3 * 4 is 2 + 3 + 3 + 3 +3

Yes it does., need to work on your comprehension..

Multiplication is defined as repeated addition - 3x4=3+3+3+3

other than that we all agree to it

You can disagree as much as you want and 3x4 will still be defined as 3+3+3+3. It's been that way ever since Multiplication was invented.

"A common mistake is to think division is prioritised above multiplication"

That is what I said. I said it's a mistake to think one of them has a precedence over the other. You're arguing the same point I'm making?

I said it’s a mistake to think one of them has a precedence over the other

And I said it's not a mistake. You still get the right answer.

You’re arguing the same point I’m making?

No, I'm telling you that prioritising either isn't a mistake. Mistakes give wrong answers. Prioritising either doesn't give wrong answers.

The arithmetic operations, addition +
, subtraction −
, multiplication ×
, and division ÷

That better? Or you can find one you like all by yourself: https://duckduckgo.com/?q=binary+operator&ko=-1&ia=web

Yes it does., need to work on your comprehension..

And you can shove the condescension up your ass until you understand the difference between unary and binary operators.

But to original point. I'm not disagreeing with anything and you're proving my point for me. There is no fundamental law of the universe that says multiplication comes first. It's defined by man and agreed to. If we encounter aliens someday, the area of their triangles are still going to be half the width times the height, the ratios of their circles circumference to diameter are still going to be pi, regardless of how they represent those values. But they could very well prioritize addition and subtraction over multiplication and division.

That better?

Is it a Maths textbook?

Or you can find one you like all by yourself

I already have dozens of Maths textbooks thanks.

And you can shove the condescension up your ass until you understand the difference between unary and binary operators

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

you’re proving my point for me.

Still need to work on your comprehension then. I did nothing of the sort.

There is no fundamental law of the universe that says multiplication comes first.

Yes there is. The fact that it's defined as repeated addition. You don't do it first, you get wrong answers.

It’s defined by man and agreed to

It's been defined and man has no choice but to agree with the consequences of the definition, or you get wrong answers.

But they could very well prioritize addition and subtraction over multiplication and division

No they couldn't. It gives wrong answers.

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 which doesn't make it a universal truth. If we're all doing it just to make things easier to understand, that implies we could have a right to left rule. It's also true that not all cultures right in the same way.

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

Lastly here is an article that also highlights the issue.

https://scienceblogs.com/evolutionblog/2013/03/15/the-horror-of-pemdas

Some of you are already insisting in your head that 6 ÷ 2(1+2) has only one right answer, but hear me out. The problem isn’t the mathematical operations. It’s knowing what operations the author of the problem wants you to do, and in what order. Simple, right? We use an “order of operations” rule we memorized in childhood: “Please excuse my dear Aunt Sally,” or PEMDAS, which stands for Parentheses Exponents Multiplication Division Addition Subtraction.* This handy acronym should settle any debate—except it doesn’t, because it’s not a rule at all. It’s a convention, a customary way of doing things we’ve developed only recently, and like other customs, it has evolved over time. (And even math teachers argue over order of operations.)