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!
That it’s wrong. If I have 1 2 litre bottle of milk, and 4 3 litre bottles of milk - i.e. 2+3x4 - how many litres of milk do I have? Without even doing the arithmetic, just count it up and tell me how many litres there is.
If we change how equations are parsed so addition comes before multiplication, 2+3x4 is not the equation required to solve that problem. 2+(3x4) is the equation needed. You can’t change how equations work and then expect all equations to work the same after the change.
If your argument is that this will add parentheses where we didn’t need them before, that’s valid and its the reason we do it this way in the first place. But that doesn’t mean there is anything fundamentally wrong with having a different system of writing equations in which operations are executed in a different order.
Our whole system of writing equations is just a convention, and yes, it is a good and easy to understand and use way of writing math. But there is no fundamental truth behind it, only that it is simpler for the majority of use cases.
People keep debating over this stuff. I have a simpler solution. Math is not real.
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” 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.
Let’s assume for a minute addition comes first. We know 2+3 is 5, and 5x4 is the same as 5+5+5+5=20. What is the issue with that?
That it’s wrong. If I have 1 2 litre bottle of milk, and 4 3 litre bottles of milk - i.e. 2+3x4 - how many litres of milk do I have? Without even doing the arithmetic, just count it up and tell me how many litres there is.
If we change how equations are parsed so addition comes before multiplication, 2+3x4 is not the equation required to solve that problem. 2+(3x4) is the equation needed. You can’t change how equations work and then expect all equations to work the same after the change.
If your argument is that this will add parentheses where we didn’t need them before, that’s valid and its the reason we do it this way in the first place. But that doesn’t mean there is anything fundamentally wrong with having a different system of writing equations in which operations are executed in a different order.
Our whole system of writing equations is just a convention, and yes, it is a good and easy to understand and use way of writing math. But there is no fundamental truth behind it, only that it is simpler for the majority of use cases.