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.
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.
No, you completely misunderstood my point. My point is not to describe all valid interpretations of the commutative property, but the one most slow kids will hear.
OFC the actual rule is the order doesn’t matter, but kids that don’t pick up on the nuance of the commutative property will still remember, “order of appearance is fine”.
Yes thank you! If you have a sum it is really great to order it in a way that makes it better to ad in your head and i think that lots of people do that without thinking about it.
X=2+3+1+6+2+4+7+5
X=2+3+5+4+6+7+1+2
X=5+5 + 10 +7+1+2
X=10 + 10 + 7+3
X=10 + 10 + 10
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)
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.
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 do, it’s grouping those operations to say that they have the same precedence
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.
Without them it implies you always do addition before subtraction, for example
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?
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.
Some other pedantic notes you may find 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 no “correct answer” to an expression without defining the order of operations on that expression
There is only one order of operations, defined in many Maths textbooks.
Addition, subtraction, etc. are mathematical necessities that must work the way they do
Hence the order of operations rules, found in Maths textbooks
But PE(MD)(AS) is something we made up
PEMDAS actually, and yes, it’s only a convention, not the rules themselves
there is no actual reason why that must be the operator precedence rule we use
That’s why it’s only a convention, and not a rule.
this is what causes issues with communicating about these things.
Nope, doesn’t cause any issues - the rules themselves are the same everywhere, and all of the different mnemonics all work
Your second example, -1+3+2=4, actually opens up an interesting can of worms
No it doesn’t
so subtraction is a-b
Just -b actually
negation is -c
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).
a two-argument definition of subtraction
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.
you can also define -1 as a single symbol
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
not as a negation operation followed by a positive one
The 1 can’t be positive if it follows a minus sign - it’s the rule of Left Associativity 😂
These distinctions are for the most part pedantic formalities
No, they’re just you spouting more wrong stuff 😂
you could argue that -1+3+2 evaluated with addition having a higher precedence than subtraction is -(1+3+2) = -6
No, you can’t. Giving addition a higher priority is +(3+2)-1=+5-1=4, as per Maths textbooks…
Conversations around operator precedence can cause real differences in how expressions are evaluated
No they can’t. The rules are universal
you might not underatand it yourself
says someone about to prove that they don’t understand it… 😂
With (AS), 3-2+1 = (3-2)+1 = 1+1 = 2
Nope! With AS 3-2+1=+(3+1)-(2)=4-2=2
This is what you would expect
Yes, I expected you to not understand what AS meant 😂
since we do generally agree to evaluate addition and subtraction with the same precedence left-to-right
It’s only a convention, not a rule, as just proven
With SA, the evaluation is the same
No it isn’t. With SA 3-2+1=-(2)+(3+1)=-2+4=2
you get the same answer
Yep, because order doesn’t matter 🙄 AS and SA both give the same answer
No issue there for this expression
Or any expression
But with AS, 3-2+1 = 3-(2+1)
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
So evaluating addition with higher precedence rather than equal precedence yields a different answer
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:
Those Brackets don’t matter. I don’t know why people insist it does
Understanding the purpose and methods of debate allows you to understand why people know the brackets matter.
I really want to have a good discussion about this
says person who deleted their previous post when I proved how wrong it was 😂
it is not possible with your debate style
There’s no debate - the rules are in Maths textbooks, which you want to pretend don’t exist
You fail to understand the argument your opponent is making
You haven’t got one. That’s why you keep pretending Maths textbooks don’t exist
By divorcing each partial statement from its surrounding context
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 😂
you are likely to change its meaning
Nope. I’m still talking about the rules of Maths 😂
You are not making a point of your own
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 are simply stating facts, opinions, or misunderstandings as if they are self-evidently true
You left out backing it up with textbook screenshots and worked examples 😂
without knowing why you believe them to be true.
There’s no belief involved. It’s easy enough to prove it yourself by doing the Maths 😂
it’s very easy to state two contradictory things without realizing it
And yet I never have. Why do you think that is? 😂
“No they can’t. The rules are universal”
Which is correct
“It’s only a convention, not a rule, as just proven”
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
this also makes it hard for people to find the mistakes
That’s because I’m not making any 😂
I can see that you don’t fully understand what I mean by “operator precedence”
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 😂
If your opponent also used this debate style,
Which you don’t, given you have no evidence whatsoever to back up your points with 😂
ends up entirely divorced from the initial meaning
I’ve been on-point the whole time, and you keep trying to deflect from how wrong your statements are 😂
Please do not take these as insults
Well, obviously not, given I just proved they were all wrong 😂
allows you to understand why people know the brackets matter.
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) 😂
Huh I just remembered the orders of arithmetic but parentheses trump all so do them first (I use them in even the calculator app). Mean I assume that’s that that says but never learned that acronym is all. Now figuring out categories of words;really does my noodle in sometimes. Cause some words can be either depending on context. Math when it’s written out has (mostly) the same answer. I say mostly because somewhere in the back of my brain there are some scenarios where something more complicated than straight arithmetic can come out oddly but written as such should come out the same.
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
Well the rule is: any order goes. Summation is commutative.
No, you completely misunderstood my point. My point is not to describe all valid interpretations of the commutative property, but the one most slow kids will hear.
OFC the actual rule is the order doesn’t matter, but kids that don’t pick up on the nuance of the commutative property will still remember, “order of appearance is fine”.
Yes thank you! If you have a sum it is really great to order it in a way that makes it better to ad in your head and i think that lots of people do that without thinking about it. X=2+3+1+6+2+4+7+5 X=2+3+5+4+6+7+1+2 X=5+5 + 10 +7+1+2 X=10 + 10 + 7+3 X=10 + 10 + 10
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?
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.
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 😂
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) 😂
Huh I just remembered the orders of arithmetic but parentheses trump all so do them first (I use them in even the calculator app). Mean I assume that’s that that says but never learned that acronym is all. Now figuring out categories of words;really does my noodle in sometimes. Cause some words can be either depending on context. Math when it’s written out has (mostly) the same answer. I say mostly because somewhere in the back of my brain there are some scenarios where something more complicated than straight arithmetic can come out oddly but written as such should come out the same.