My mom’s a mathematician, she got annoyed when I said that the order of operations is just arbitrary rules made up by people a couple thousand years ago
It’s organized so that more powerful operations get precedence, which seems natural.
Set aside intentionally confusing expressions. The basic idea of the Order of Operations holds water even without ever formally learning the rules.
If an addition result comes first and gets exponentiated, the changes from the addition are exaggerated. It makes addition more powerful than it should be. The big stuff should happen first, then the more granular operations. Of course, there are specific cases where we need to reorder, or add clarity, which is why human decisions about groupings are at the top.
The big stuff should happen first, then the more granular operations
The “big stuff” is stuff that is defined in terms of something else. i.e. exponents are shorthand for repeated multiplication… and multiplication is shorthand for repeated addition, hence they have to be done in that order or you get wrong answers.
“Wrong answers” only according to our current order of operations, math still works if you, for example, make additions come first (as long as you’re consistent about it).
OFC it is a convention and to change it you would have to change all expressions ever written all at the same time, to avoid confusion between competing standards. I’m not arguing that it should be changed, only that there is no ‘high truth’ behind it.
“Wrong answers” only according to our current order of operations
No, according to arithmetic.
math still works if you, for example, make additions come first
No, it doesn’t - order of operations proof. The only way it could work with addition first is if we swapped the definitions of addition and multiplication around… but then we still have the same order of operations, all we’ve done is swapped around what we call addition and multiplication!
My mom’s a mathematician, she got annoyed when I said that the order of operations is just arbitrary rules made up by people a couple thousand years ago
I’m not surprised. Here’s the proof of the order of operations rules. Also, the equals sign wasn’t invented until the 16th century, so only 500 years old at most (the earliest references to order of operations are over 400 years ago).
That proof for the order of operations sure seems to rely a lot on our current order of operations
Doesn’t use order of operations at all. It only uses the definitions of the operators. i.e. 3x4=3+3+3+3 by definition. i.e. nothing to do with order of operations.
If I have 1 2l bottle of milk, and 4 3l bottles of milk, how many litres of milk do I have? It can be solved by simply adding them up - again, nothing to do with order of operations here, just simple addition. Now, write it out as a mathematical expression which uses multiplication, and tell me which order of operations gets you the right answer. Voila! Welcome to how we worked out what the order of operations rules had to be.
“Math” is a mass noun. You can’t have “a math”. It’s like blood or love. You can have more blood or less blood. There might be units in which blood is measured that you can have a certain number of (“a gallon of blood”), but you can’t have, unqualified, a blood or two bloods (well, not in that sense of the word, anyway).
People keep debating over this stuff. I have a simpler solution. Math is not real.
The only real answer lmao. People really out here thinking the funny symbols on the paper follow absolute laws. Crazy.
They do. Maths is universal, just like the laws of Physics (which are often written using Maths BTW).
My mom’s a mathematician, she got annoyed when I said that the order of operations is just arbitrary rules made up by people a couple thousand years ago
It’s organized so that more powerful operations get precedence, which seems natural.
Set aside intentionally confusing expressions. The basic idea of the Order of Operations holds water even without ever formally learning the rules.
If an addition result comes first and gets exponentiated, the changes from the addition are exaggerated. It makes addition more powerful than it should be. The big stuff should happen first, then the more granular operations. Of course, there are specific cases where we need to reorder, or add clarity, which is why human decisions about groupings are at the top.
Yeah, but that’s why I like to buff my base attack before I invest in multipliers and armor penetration!
The “big stuff” is stuff that is defined in terms of something else. i.e. exponents are shorthand for repeated multiplication… and multiplication is shorthand for repeated addition, hence they have to be done in that order or you get wrong answers.
“Wrong answers” only according to our current order of operations, math still works if you, for example, make additions come first (as long as you’re consistent about it).
OFC it is a convention and to change it you would have to change all expressions ever written all at the same time, to avoid confusion between competing standards. I’m not arguing that it should be changed, only that there is no ‘high truth’ behind it.
No, according to arithmetic.
No, it doesn’t - order of operations proof. The only way it could work with addition first is if we swapped the definitions of addition and multiplication around… but then we still have the same order of operations, all we’ve done is swapped around what we call addition and multiplication!
There is when it comes to order of operations.
I’m not surprised. Here’s the proof of the order of operations rules. Also, the equals sign wasn’t invented until the 16th century, so only 500 years old at most (the earliest references to order of operations are over 400 years ago).
That proof for the order of operations sure seems to rely a lot on our current order of operations…
Doesn’t use order of operations at all. It only uses the definitions of the operators. i.e. 3x4=3+3+3+3 by definition. i.e. nothing to do with order of operations.
If I have 1 2l bottle of milk, and 4 3l bottles of milk, how many litres of milk do I have? It can be solved by simply adding them up - again, nothing to do with order of operations here, just simple addition. Now, write it out as a mathematical expression which uses multiplication, and tell me which order of operations gets you the right answer. Voila! Welcome to how we worked out what the order of operations rules had to be.
I’m with you. Has anyone ever actually seen a math? Can you buy a math at the math store? Are there bespoke math craftspeople?
No.
I rest my case.
Is math in the room with us right now?
“Math” is a mass noun. You can’t have “a math”. It’s like blood or love. You can have more blood or less blood. There might be units in which blood is measured that you can have a certain number of (“a gallon of blood”), but you can’t have, unqualified, a blood or two bloods (well, not in that sense of the word, anyway).
You know this is 196, right?
You know we are adults who live in the real world, right?
I don’t think you understand the concept of shitposting.
No, you have a branch of Mathematics.