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.

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.

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.

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.

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

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! 😂

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.

For me it’s the arguments when there is a parentheses but no operator (otherwise known as implied multiplication)

No, it's known as Factorised Terms/Products, solved via The Distributive Law, a(b+c)=(ab+ac). "implied multiplication" is a made up rule by people who have forgotten the actual rules, and often they get it wrong (because, having wrongly called it "multiplication", they then wrongly give it the precedence of multiplication, not brackets).

they aren’t teaching math.

Yes we are. Adults forgetting it is another matter altogether.

There’s no such thing as “order of operations” in math

Yes there is! 😂

Do you think I’m wrong?

No, I know you're wrong.

If so, why?

If you don't solve binary operators before unary operators you get wrong answers. 2+3x4=14, not 20. 3x4=3+3+3+3 by definition

A division is defined as a multiplication

No it isn't. Multiplication is defined as repeated addition. Division isn't repeated subtraction. They just happen to have opposite effects if you treat the quotient as being the result of dividing.

you can prove it with math

Not a proof, just wrong. In the "(substitute 0.9999… = x)" step, it was only done to one side, not both (the left side would've become 9.99999), therefore wrong.

order?

It's actually short for "to the order of", as in 2 squared is 2 to the order of 2. i.e. same thing as Exponent or Index.