No worries :-)
SmartmanApps
joined 2 years ago
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?
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.
The person who couldn't even manage to get 10-1+1 correct when doing addition first 😂