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Some people insist there's no "correct" order for the basic arithmetic operations. And worse, some people insist the correct order is parenthesis first, then left to right.
Both of those sets of people are wrong.
And those people are wrong
As per Maths textbooks
All Maths textbooks are wrong?? 😂
Hopefully you can see where their confusion might come from, though. PEMDAS is more P-E-MD-AS. If you have a bunch of unparenthesized addition and subtraction, left to right is correct. A lot of like, firstgrader math problems are just basic problems that are usually left to right (but should have some extras to highlight PEMDAS somewhere I'd hope).
So they're mostly telling you they only remember as much math as a small child that barely passed math exercizes.
You can do addition and subtraction in any order and it's still correct
If you have a bunch of unparenthesized addition and subtraction, left to right doesn't matter.
1 + 2 + 3 = 3 + 2 + 1
True, but as with many things, something has to be the rule for processing it. For many teachers as I've heard, order of appearance is 'the rule' when commutative properties apply. ... at least until algebra demands simplification, but that's a different topic.
That's because students often make mistakes with signs when they do it in a different order, so we tell them to stick to left to right
Right, because 1-2-3=3-2-1.
No, 1-2-3=-3-2+1. You changed the signs on the 1 and the 3.
You flipped the sign on the 3 and 1.
I did not flip any signs, merely reversed the order in which the operations are written out. If you read the right side from right to left, it has the same meaning as the left side from left to right.
Hell, the convention that the sign is on the left is also just a convention, as is the idea that the smallest digit is on the right (which should be a familiar issue to programmers, if you look up big endian vs little endian)
Yes you did! 😂
No, merely reversing the order gives -3-2+1 - you changed the signs on the 1 and 3.
Starts with -3, which you changed to +3
when you don't change any of the signs it does 😂
Nope, it's a rule of Maths, Left Associativity.
If that's your idea of reversing the order, then you're not talking about the same thing as SpaceCadet@feddit.nl. They're talking about the order of operations and the associativity/commutativity property. You're talking about the order of the symbols.
PE(MD)(AS)
Now just remember to account for those parentheses first...
Those Brackets don't matter. I don't know why people insist it does
They do, it's grouping those operations to say that they have the same precedence. Without them it implies you always do addition before subtraction, for example.
They don't. It's irrelevant that they have the same priority. MD and DM are both correct, and AS and SA are both correct. 2+3-1=4 is correct, -1+3+2=4 is correct.
And there's absolutely nothing wrong with doing that, for example. You still always get the correct answer 🙄
Uh, no. I don't think you've thought this through, or you're just using (AS) without realizing it. Conversations around operator precedence can cause real differences in how expressions are evaluated and if you think everyone else is just being pedantic or is confused then you might not underatand it yourself.
Take for example the expression 3-2+1.
With (AS), 3-2+1 = (3-2)+1 = 1+1 = 2. This is what you would expect, since we do generally agree to evaluate addition and subtraction with the same precedence left-to-right.
With SA, the evaluation is the same, and you get the same answer. No issue there for this expression.
But with AS, 3-2+1 = 3-(2+1) = 3-3 = 0. So evaluating addition with higher precedence rather than equal precedence yields a different answer.
=====
Some other pedantic notes you may find interesting:
There is no "correct answer" to an expression without defining the order of operations on that expression. Addition, subtraction, etc. are mathematical necessities that must work the way they do. But PE(MD)(AS) is something we made up; there is no actual reason why that must be the operator precedence rule we use, and this is what causes issues with communicating about these things. People don't realize that writing mathematical expressions out using operator symbols and applying PE(MD)(AS) to evaluate that expression is a choice, an arbitrary decision we made, rather than something fundamental like most everything else they were taught in math class. See also Reverse Polish Notation.
Your second example, -1+3+2=4, actually opens up an interesting can of worms. Is negation a different operation than subtraction? You can define it that way. Some people do this, with a smaller, slightly higher subtraction sign before a number indicating negation. Formal definitions sometimes do this too, because operators typically have a set number of arguments, so subtraction is a-b and negation is -c. This avoids issues with expressions starting with a negative number being technically invalid for a two-argument definition of subtraction. Alternatively, you can also define -1 as a single symbol that indicates negative one, not as a negation operation followed by a positive one. These distinctions are for the most part pedantic formalities, but without them you could argue that -1+3+2 evaluated with addition having a higher precedence than subtraction is -(1+3+2) = -6. Defining negation as a separate operation with higher precedence than addition or subtraction, or just saying it's subtraction and all subtraction has higher prexedence than addition, or saying that -1 is a single symbol, all instead give you your expected answer of 4. Isn't that interesting?
It's hilarious that you added in this in afterwards, hoping I wouldn't see it so you could claim the last word 😂
There is only one order of operations, defined in many Maths textbooks.
Hence the order of operations rules, found in Maths textbooks
PEMDAS actually, and yes, it's only a convention, not the rules themselves
That's why it's only a convention, and not a rule.
Nope, doesn't cause any issues - the rules themselves are the same everywhere, and all of the different mnemonics all work
No it doesn't
Just -b actually
Which is still subtraction, from 0, because every operation on the numberline starts from 0, we just don't bother writing the zero (just like we don't bother writing the + sign when the expression starts with an addition).
Subtraction is unary operator, not binary. If you're subtracting from another number, then that number has it's own operator that it's associated with (and might be an unwritten +), it's not associated with the subtraction at all.
No you can't. You can put it in Brackets to make it joined to the minus sign though, like in (-1)²=1, as opposed to -1²=-1
The 1 can't be positive if it follows a minus sign - it's the rule of Left Associativity 😂
No, they're just you spouting more wrong stuff 😂
No, you can't. Giving addition a higher priority is +(3+2)-1=+5-1=4, as per Maths textbooks...
No, all of it was wrong, again 😂
I'm honestly disappointed that you just downvoted and left. Challenging your beliefs with contrary ideas is the only way to improve them and understand the world in a more comprehensive and accurate way.
as per the textbooks 🙄
No they can't. The rules are universal
says someone about to prove that they don't understand it... 😂
Nope! With AS 3-2+1=+(3+1)-(2)=4-2=2
Yes, I expected you to not understand what AS meant 😂
It's only a convention, not a rule, as just proven
No it isn't. With SA 3-2+1=-(2)+(3+1)=-2+4=2
Yep, because order doesn't matter 🙄 AS and SA both give the same answer
Or any expression
You just violated the rules and changed the sign of the 1 from a + to a minus. 🙄 -(2+1)=-2-1, not -2+1. Welcome to how you got a wrong answer when you wrongly added brackets to it and mixed the different signs together
No it doesn't., as already proven. 3-2+1=+(3+1)-(2)=+4-2=2, same answer 🙄
Oh, it's you. I really want to have a good discussion about this, but it is not possible with your debate style. Once again, fragmenting your opponent's argument into a million partial statements and then responding to those is ineffective for several reasons:
You fail to understand the argument your opponent is making, and so you do not learn anything by engaging with it. You must first understand to learn.
By divorcing each partial statement from its surrounding context, you are likely to change its meaning, so you are no longer even responding to the meaning of what was said.
You are not making a point of your own, which means you are less likely to figure out your own mental model. You are simply stating facts, opinions, or misunderstandings as if they are self-evidently true, without knowing why you believe them to be true.
Expanding on point three, it's very easy to state two contradictory things without realizing it. For example, "No they can’t. The rules are universal" and "It’s only a convention, not a rule, as just proven".
Also expanding on point three, this also makes it hard for people to find the mistakes you're making and correct them, because mistakes in your mental model are only visible through the statements you choose to make, which are incoherent when taken together. For example, I can see that you don't fully understand what I mean by "operator precedence", but this is not obvious from your main point, because you have no main point, because you do not understand what mine is.
If your opponent also used this debate style, the argument takes hours and ends up entirely divorced from the initial meaning, completely destroying any hope of having the debate provide any actual value, ie. greater understanding.
Please do not take these as insults; it's a long shot to fundamentally change someone's perspective like this in one post, but I would love if you saw the beauty of discussion. To bring it back to your original comment:
Understanding the purpose and methods of debate allows you to understand why people know the brackets matter.
says person who deleted their previous post when I proved how wrong it was 😂
There's no debate - the rules are in Maths textbooks, which you want to pretend don't exist
You haven't got one. That's why you keep pretending Maths textbooks don't exist
says person who deleted one of their posts to remove the context. 😂 The context is the rules of Maths, in case you needed to be reminded 😂
Nope. I'm still talking about the rules of Maths 😂
Ok, so here you are admitting to comprehension problems. Which part did you not understand in addition and subtraction can be done in any order? 😂
You left out backing it up with textbook screenshots and worked examples 😂
There's no belief involved. It's easy enough to prove it yourself by doing the Maths 😂
And yet I never have. Why do you think that is? 😂
Which is correct
Which is also correct, and in no way contradicts the previous point, and I have no idea why you think it does! 😂 The first point is about the rules, and the second point is about conventions, which isn't even the same thing
That's because I'm not making any 😂
Says person who in their other post claimed "addition first" for -1+3+2 is -(1+3+2) = -6, and not +(3+2)-1=4 😂
Which you don't, given you have no evidence whatsoever to back up your points with 😂
I've been on-point the whole time, and you keep trying to deflect from how wrong your statements are 😂
Well, obviously not, given I just proved they were all wrong 😂
Except I've proven, repeatedly, that they don't, and so now you're trying to deflect from that (and deleted one of your posts to hide the evidence of how wrong you are) 😂
I'm falling for the troll here but I feel compelled to point out that you did NOT read the post I deleted lmao. I deleted it because I posted it before you "responded" to my points. Go check it out, I just restored it.
I should clarify that I haven't responded to your "points" because there is nothing worth responding to. Your arguments can all be debunked by reading https://en.wikipedia.org/wiki/Order_of_operations, so I didn't bother doing it myself.
To avoid any further temptation to respond I will be blocking you. Your absence from my future will be greatly appreciated. I feel that the deleted post is in itself a very good final word to this disappointment of a "conversation" even if it is not entirely accurate. Goodbye.
Just as well for you I've provided all the necessary evidence to prove them wrong then
BWAHAHAHAHAHA! I DIDN'T leave, quite demonstrably.
So how come you won't then?
In other words, you have been proven wrong by them
Wikipedia can be comprehensively debunked by MATHS TEXTBOOKS - you know, those things you refuse to look at because they prove you are wrong 😂
So in other words, Wikipedia is all you had, and, having been disproven by Maths textbooks, you've got nothing
An admission of defeat then
Feel free to unblock me when you're ready to take your own advice
Just like all your other posts then
Don't let the door hit you on the way out
Well, this is just a writing standard that is globally agreed on,
The writing rules are defined by humans not by natural force
(That one thing and another thing are two things, is a rule from nature, as comparison)
Save yourself the trouble - Smartman Apps is a crank. They categorically will not comprehend the difference between the notation we made up and how numbers work. Dingus keeps saying 'animals can count' like that proves parentheses-first is completely different! from distribution.
Why'd Russel and Whitehead bother with the Principia Mathematica when they could just point to Clever Hans?
No, it's a universal rule of Maths
Maths is for describing natural forces, and is subject to those laws
Yep, there are even some animals who understand that, and all of Maths is based upon it.
I mean, arithmetic order is just convention, not a mathematical truth. But that convention works in the way we know, yes, because that's what's.. well.. convention
Nope, rules arising from the definition of the operators in the first place.
It most certainly is a mathematical truth!
The mnemonics are conventions, the rules are rules
The rules are socially agreed upon. They are not a mathematical truth. There is nothing about the order of multiple different operators in the definition of the operators themselves. An operator is simply just a function or mapping, and you can order those however you like. All that matters is just what calculation it is that you're after
Nope! Universal laws.
Yes they are! 😂
That's exactly where it is. 2x3 is defined as 2+2+2, therefore if you don't do Multiplication before Addition you get wrong answers
No you can't! 😂 2+3x4=5x4=20, Oops! WRONG ANSWER 😂
And if you want the right answer then you have to obey the order of operations rules
That's a very simplistic view of maths. It's convention https://en.wikipedia.org/wiki/Order_of_operations
Just because a definition of an operator contains another operator, does not require that operator to take precedence. As you pointed out, 2+3*4 could just as well be calculated to 5*4 and thus 20. There's no mathematical contradiction there. Nothing broke. You just get a different answer. This is all perfectly in line with how maths work.
You can think of operators as functions, in that case, you could rewrite 2+3*4 as add(2, mult(3, 4)), for typical convention. But it could just as well be mult(add(2, 3), 4), where addition takes precedence. Or, similarly, for 2*3+4, as add(mult(2, 3), 4) for typical convention, or mult(2, add(3, 4)), where addition takes precedence. And I hope you see how, in here, everything seems to work just fine, it just depends on how you rearrange things. This sort of functional breakdown of operators is much closer to mathematical reality, and our operators is just convention, to make it easier to read.
Something in between would be requiring parentheses around every operator, to enforce order. Such as (2+(3*4)) or ((2+3)*4)
The Distributive Law and Arithmetic is very simple.
Nope, a literal Law. See screenshot
Isn't a Maths textbook, and has many mistakes in it
Yes it does 😂
2+3x4=2+3+3+3+3=14 by definition of Multiplication
2+3x4=5x4=20 Oops! WRONG ANSWER 😂
No, I pointed out that it can't be calculated like that, you get a wrong answer, and you get a wrong answer because 3x4=3+3+3+3 by definition
Just a wrong answer and a right one. If I have 1 2 litre bottle of milk, and 4 3 litre bottles of milk, even young kids know how to count up how many litres I have. Go ahead and ask them what the correct answer is 🙄
You got a wrong answer when you broke the rules of Maths. Spoiler alert: I don't have 20 litres of milk
A provably wrong answer 😂
2+3x4=20 is not in line with how Maths works. 2+3+3+3+3 does not equal 20 😂
rule
And it gives you a wrong answer 🙄 I still don't have 20 litres of milk
No, I see quite clearly that I have 14 litres of milk, not 20 litres of milk. Even a young kid can count up and tell you that
Correctly or not
The notation is, the rules aren't
No it wouldn't. You know we've only been using brackets in Maths for 300 years, right? Order of operations is much older than that
Which is exactly how they did it before we started using Brackets in Maths 😂 2+3x4=2+3+3+3+3=14, not complicated.
I mean, it is pretty clear here that you do not really understand the purpose of notation, nor what maths is. Notation is just a constructed language to convey a mathematical idea, it's malleable
And yeah, it's easy to just say "this page is wrong!" without any further argument. Nothing you referenced proved the convention as law, and neither is there any mathematical basis for any proof, because it simply is nonsensical to "prove" a notation. Have another source for this being convention https://www.themathdoctors.org/order-of-operations-why/ or https://math.stackexchange.com/questions/884765/mathematical-proof-for-order-of-operations. If you want a book about this, then there's https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev that is cited by wikipedia. I'm sure you could also find stuff about this in a set theory book. Though good luck understanding them without sufficient experience in high-level maths
Really though, maths is so much more than "3+5=8 because that's the correct answer!" But why is it the correct answer? In what context? What is the definition of addition? How can you prove that 1+1=2 from fundamental axioms? This is harder to answer than you might think.
says person who doesn't understand that there is only one possible answer to 2+3x4. Even kids who are still counting up know what it is
Yep, and the rules aren't. 2+3x4 can only ever equal 14. In Germany it's written 2+3.4, and it's still equal to 14, because the rules are universal
says person ignoring the textbook screenshots explaining why it's a Law 🙄
Yes there is. See textbook screenshots 🙄
It proves the rules 🙄
Read the comments and you'll find multiple people telling him he is wrong, with references 😂 His usual comeback is "well, that doesn't prove that it's taught everywhere", yeah only that they ALL say the same thing! 😂 And he even admitted at one point he couldn't find his rule in any Maths textbooks. 😂 I even tried to tell him myself, and he deleted my comment because I proved he was wrong 😂
Is well-known to be overridden with people who do not know how to do order of operations 😂 On Mastodon I've seen people asking where is a better place to take Maths problems
I have plenty of Maths textbooks, which for some reason you refuse to look in
"comprehensive handbook" - so, yet again, not a Maths textbook 🙄
"first published in 1945 in Russia" - the order of operations rules are older than 1945 😂
"frequently used guide for scientists, engineers, and technical university students" - notably no mention of Mathematicians
and you could find this in a high school Maths textbook
You know teachers here are required to have a Masters in Maths right?? 😂
Count up and find out, or use some Cuisenaire rods. This is how young kids learn to do it
The context of Addition 🙄
1+1=2, then inductively proven for all subsequent numbers
It's true by definition
Not hard at all. 1+1=2 by definition, then the rest of the numbers are proven inductively. You know there are several species of animals that also know how to count, right?
Maths is so much more malleable and abstract than what you think it is. You really do not understand maths as well as you think you do, and I feel a bit sad for any student of yours that would wish to explore some deeper revelations of maths, just to be told "nope! That's just how it is!" with no further thinking at all.
A lot of maths is chosen. Choices with good motivation, but choices nonetheless. So long as there not being contradictions or paradoxes, the formulation of a form of math is valid. Which is why you have different forms of maths with different rules.
And you really could use some more humility, it's obnoxious when you act all so high and mighty and arrogant, with no interest in questioning your assumptions. Devolving into ridiculing the person you're discussing with and a general vibe of "omfg I'm right you fucking idiot because I'm right how dumb can you get??"
Like, what is it that you want here, a book from the 700s of the one dude that invented arithmetics and told clearly "I chose this."? You are making your arguments effectively unfalsifiable by just going "Nuh uh" all the time.
Get some humility and learn a bit about the foundations of maths. Like. Down to set theory. See for yourself what actually is the foundation. And, spoiler, it's not a high school textbook. Hopefully I do not need to tell you how concepts are simplified for younger students, instead of overwhelming them with the complete knowledge of a subject.
No it isn't, as per Maths textbooks
says someone who doesn't understand it at all
Just as well I'm their teacher then, hey? 😂 I showed you the textbooks, and you refused to look at them
Nope! Only the notation.
You mean so long as it obeys the laws of nature
But we don't have different rules, only different notations. The rules of Maths are universal
says person who refuses to look in Maths textbooks
says person who refuses to look in Maths textbooks
there aren't any. All the rules of Maths are explicitly spelt out in Maths textbooks, not to mention several of which are easy to prove.
Like the person who refuses to look in Maths textbooks
No-one chose it. There are even several species of animals that know how to count! 😂 It's a universal law
Just as well I also provide the proof in the form of Maths textbooks. Oh wait, you keep refusing to look at them! 😂
says person who refuses to look in Maths textbooks
says person who knows nothing about it. Makes up fanciful stories like it was "chosen" when nature proves otherwise
It's Arithmetic. Even some animals know how to do Arithmetic, none of them know how to do set theory! 😂
That's right, it's a Primary school textbook 😂
And yet you still manage to not understand them 🙄
Welcome to why Algebra isn't taught until Year 7 😂
Social conventions are real, well defined things. Some mathematicians like to pretend they aren't, while using a truckload of them; that's a hypocritical opinion.
That's not to say you can't change them. But all of basic arithmetic is a social convention, you can redefine the numbers and operations any time you want too.
So are the laws of nature, that Maths arises from
No, you making false accusations against Mathematicians is a strawman
You can change the conventions, you cannot change the rules
Nope, law of nature. Even several animals know how to count.
And you end up back where you started, since you can't change the laws of nature