lemm.ee

1 point

8 months ago

“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!

there is no ‘high truth’ behind it.

There is when it comes to order of operations.

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AdrianTheFrog@lemmy.world

[ - ]

1 point

7 months ago

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?

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[ - ]

1 point

7 months ago

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.

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AdrianTheFrog@lemmy.world

[ - ]

1 point

7 months ago

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.

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[ - ]

1 point

7 months ago

Noted that you didn’t answer my question - the answer is I have 14 litres of milk. 2+3+3+3+3=14 litres. When you did “arbitrary addition first”, you got 20, which is wrong, which is why no other order of operations rules work than the ones we have.

You can’t change how equations work and then expect all equations to work the same after the change

In actual fact the point is that they will except for what ever your new notation is. e.g. if we instead defined + to mean multiply, and x to mean add, then we would do + before x, and again, that would be the only order of operations which works. i.e. the only order which gives us 14 litres.

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

No, and if you did that, you would again arrive at only one order of operations rules which works, cos I still have 14 litres, and the Maths in this new system still has to give an answer of 14 litres, not 20.

Our whole system of writing equations is just a convention

Nope, it’s all rules, found in any Maths textbook, and if you don’t obey the rules you get wrong answers (like you did when you got 20).

But there is no fundamental truth behind it

Yes there is - I have 14 litres, and only 1 set of order of operations rules gives that answer.

only that it is simpler for the majority of use cases

If you follow the rules of Maths then it is correct for every use case. That’s why they exist in the first place.

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AdrianTheFrog@lemmy.world

[ - ]

1 point

7 months ago

I think you misunderstand my argument. I could use still math to solve a real-world problem with an altered order of operations. You could still do anything you can do with regular math, if you had a different order of operations. You could make a programming language that parses your inputted expressions with a different order of operations and still use it to calculate collisions or render a 3d scene or do anything else that involves math. Do you need me to calculate something, to prove it to you?

The order of operations is just part of a system of notation and any system of notation that exists in the world is inherently arbitrary. The same way the way that how we draw the number 3 or the number 5 has no inherent meaning behind it other than the convention of how we interpret it, the order of operations is nothing more than a standard part of the notation. Again, I’m not saying that we should or could change it, as there would be no way to indicate which convention we are using and the standard order of operations works perfectly fine.

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[ - ]

1 point

7 months ago

I think you misunderstand my argument

No, you demonstrably didn’t understand mine, which is, what you are saying is impossible, but you’re still saying it’s possible.

I could use still math to solve a real-world problem with an altered order of operations

No, you can’t. You already tried to do addition first in 2+3x4 and found out why it doesn’t work. Ever since then you’ve been ignoring that result and pretending that there’s some other way to make it work. No, there isn’t. As long as multiplication is defined in terms of addition (i.e. 3x4=3+3+3+3) then it’s impossible to get a right answer unless you do multiplication before addition.

You could still do anything you can do with regular math, if you had a different order of operations

No, you can’t. Again, you already proved you can’t.

Do you need me to calculate something, to prove it to you?

Go ahead - I’m not holding my breath. I already told you why it literally can’t work. But note that adding brackets isn’t changing the order of operations - brackets are already part of the order of operations. Writing 2+3x4 as 2+(3x4) is exactly the same thing.

BTW just to FURTHER prove your “addition first” doesn’t work, look at this example…

3x4+2=3x6=18. But earlier you did 2+3x4=5x4=20 - not even the same answer in an “addition first” world! Welcome to why it’s impossible to make addition-first work. But knock yourself out - you’re welcome to try! 😂

The order of operations is just part of a system of notation

No, it isn’t. It’s part of the rules of Maths. Notation is how you write it - underlying that is how Maths actually works. This is embodied in the rules of Maths.

is inherently arbitrary

Completely fixed, and a result of the way the operators are defined - that was the only “arbitrary” bit, deciding what the operators were and what they were going to mean, but once you did that then the order of operations rules were already written for you (having already been determined as soon as you made the definitions of the operators in the first place).

number 5 has no inherent meaning behind it other than the convention of how we interpret it

Again, not a convention, a rule of how to interpret it. You can’t just decide to interpret 5 as four, or again, you end up with wrong answers. The rules of Maths prevent you from getting wrong answers. You found that out yourself when you tried to do addition first in 2+3x4.

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