💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱
- 3 Posts
- 44 Comments
11·1 day agoIt 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.
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 😂
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.
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.
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.
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.
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.
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?
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.
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).
Oh, but of course the statement changes if you add parentheses
It sure does, but they don’t seem to understand that.
Welcome to it’s not a textbook (and it wasn’t about order of operations anyway).
We also have this thing called textbooks, that schools order so that Maths classes don’t have to be held in computer labs.
And the college doesn’t teach order of operations.
by someone who can’t back up their statements with actual textbooks.
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.
Yeah, their programmers didn’t know The Distributive Law either.
Happy to take that bet. Guarantee you neither of them has studied order of operations since they were in high school.
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.
Yep, the ones with more inputs, binary operators, have to be solved first.
Says person who’s forgotten why we were talking about it to begin with! 😂
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.
which is always. As usual, the comprehension issue is at your end.
Yes it is 😂
That you still have comprehension issues? I knew that already
The name of the book is in the top left. Not very observant either.
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. 😂
Yes it is! 😂
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.
You don’t. Both need 2 Terms with signs. In this case +2 and +3.
Yep, corresponding to the 2 plus signs, +2 and +3. 1 unary operator, 1 Term, 2 of each.
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.
The real question is did you?
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).
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.
Nope, not an operation either.
I see you don’t know how grouping symbols work either.
Grouping symbols are neither.
You were the one who incorrectly brought grouping symbols into it, not me.
You haven’t provided any yet! 😂
Glad you finally admitted you have no supporting evidence. Bye then! 😂