SmartmanApps

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.

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?

I am not going to argue with you about it

Nor should you. I'm a Maths teacher.

This was resolved almost a month ago

And yet you still don't understand what's wrong with what you said.

Read the original equation again, plug some numbers into it, and try again.

That's what you need to do. You're the one coming up with wrong answers when you change the order. Changing the order doesn't change the answer.

If you still don’t get it I cannot help you

It's not me who doesn't get it. I teach it.

The brackets are used to make the equation look cleaner

No, they're used to show deviations from the usual order of operations. If I want 2+3x4 to equal 20, then I have to write (2+3)x4.

10 - 1 + 1 = 8 doing the addition first

No it isn't. 10+1-1=11-1=10 is doing the addition first. Note same answer. You in fact did 10-(1+1) - you added brackets which changed the answer, thus a wrong answer

10 - 1 - 1 = 8 regardless of order because it is all subtraction

Not all of it. You're forgetting the 10 is really +10. -10-1-1 would be all subtraction. +10-1-1 is addition and subtraction.

it is not the same regardless of order

Yes it is! 😂 It is always the same regardless of order, as I have just shown you, again.

10-1+1=9+1=10

10+1-1=11-1=10

-1+1+10=0+10=10

1-1+10=0+10=10

1+10-1=11-1=10

-1+10+1=9+1=10

you do it left to right making it incorrect to do 1-1 first.

It's NOT incorrect to do 10-1+1 or 10+1-1. It IS incorrect to do 10-(1+1), which is what you did

By doing it out of order and incorrectly I was able to make my statement true

It was solely because you did it incorrectly. Order doesn't change anything.

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.

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).

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.

÷ could be a minus sign

No it couldn't.

https://en.wikipedia.org/wiki/Division_sign?wprov=sfla1

Did you check the reference? It says % can be used as a minus sign, not the obelus. Welcome to what happens when you're next-door neighbour Joe Blow can edit Wikipedia.

Another common issue is thinking “parentheses go first”

There's no "think" - it's an absolute rule.

then beginning by solving the operation beside them

a(b) isn't an operation - it's a Product. a(b)=(axb) per The Distributive Law.

(mostly multiplication)

NOT Multiplication, a Product/Term.

The point being that what’s inside the parentheses goes first, not what’s beside them

Nope, it's the WHOLE Bracketed Term. a/bxc=ac/b, but a/b( c )=a/(bxc). Inside is only a "rule" in Elementary School, when there isn't ANYTHING next to them (students aren't taught this until High School, in Algebra), and it's not even really a rule then, it's just that there isn't anything ELSE involved in the Brackets step than what is inside (since they're never given anything on the outside).