SkyeStarfall comments on I dunno

[–] SkyeStarfall@lemmy.blahaj.zone 2 points 9 months ago (2 children)

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

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[–] SmartmanApps@programming.dev -1 points 8 months ago (1 child)

I mean, arithmetic order is just convention

Nope, rules arising from the definition of the operators in the first place.

not a mathematical truth

It most certainly is a mathematical truth!

But that convention works in the way we know, yes, because that’s what’s… well… convention

The mnemonics are conventions, the rules are rules

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[–] SkyeStarfall@lemmy.blahaj.zone 0 points 8 months ago (1 child)

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

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[–] SmartmanApps@programming.dev 0 points 8 months ago (1 child)

The rules are socially agreed upon

Nope! Universal laws.

They are not a mathematical truth.

Yes they are! 😂

There is nothing about the order of multiple different operators in the definition of the operators themselves

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

you can order those however you like.

No you can't! 😂 2+3x4=5x4=20, Oops! WRONG ANSWER 😂

All that matters is just what calculation it is that you’re after

And if you want the right answer then you have to obey the order of operations rules

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[–] SkyeStarfall@lemmy.blahaj.zone 1 point 8 months ago (1 child)

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)

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[–] SmartmanApps@programming.dev -1 points 8 months ago (1 child)

That’s a very simplistic view of maths

The Distributive Law and Arithmetic is very simple.

It’s convention

Nope, a literal Law. See screenshot

https://en.wikipedia.org/wiki/Order_of_operations

Isn't a Maths textbook, and has many mistakes in it

Just because a definition of an operator contains another operator, does not require that operator to take precedence

Yes it does 😂

2+3x4=2+3+3+3+3=14 by definition of Multiplication

2+3x4=5x4=20 Oops! WRONG ANSWER 😂

As you pointed out, 2+34 could just as well be calculated to 54 and thus 20

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

There’s no mathematical contradiction there

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 🙄

Nothing broke

You got a wrong answer when you broke the rules of Maths. Spoiler alert: I don't have 20 litres of milk

You just get a different answer

A provably wrong answer 😂

This is all perfectly in line with how maths work

2+3x4=20 is not in line with how Maths works. 2+3+3+3+3 does not equal 20 😂

add(2, mult(3, 4)), for typical

rule

But it could just as well be mult(add(2, 3), 4), where addition takes precedence

And it gives you a wrong answer 🙄 I still don't have 20 litres of milk

And I hope you see how, in here, everything seems to work just fine

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

it just depends on how you rearrange things

Correctly or not

our operators is just convention

The notation is, the rules aren't

Something in between would be requiring parentheses around every operator, to enforce order

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

Such as (2+(3*4))

Which is exactly how they did it before we started using Brackets in Maths 😂 2+3x4=2+3+3+3+3=14, not complicated.

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[–] SkyeStarfall@lemmy.blahaj.zone 1 point 8 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev -2 points 8 months ago (1 child)

I mean, it is pretty clear here that you do not really understand the purpose of notation,

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

Notation is just a constructed language to convey a mathematical idea, it’s malleable

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

Nothing you referenced proved the convention as law

says person ignoring the textbook screenshots explaining why it's a Law 🙄

neither is there any mathematical basis for any proof

Yes there is. See textbook screenshots 🙄

it simply is nonsensical to “prove” a notation

It proves the rules 🙄

Have another source for this being convention https://www.themathdoctors.org/order-of-operations-why/

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 😂

or https://math.stackexchange.com/questions/884765/mathematical-proof-for-order-of-operations.

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

If you want a book about this

I have plenty of Maths textbooks, which for some reason you refuse to look in

there’s https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev that is cited by wikipedia.

"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

I’m sure you could also find stuff about this in a set theory book

and you could find this in a high school Maths textbook

Though good luck understanding them without sufficient experience in high-level maths

You know teachers here are required to have a Masters in Maths right?? 😂

But why is it the correct answer?

Count up and find out, or use some Cuisenaire rods. This is how young kids learn to do it

In what context?

The context of Addition 🙄

What is the definition of addition?

1+1=2, then inductively proven for all subsequent numbers

How can you prove that 1+1=2 from fundamental axioms?

It's true by definition

This is harder to answer than you might think

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?

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[–] SkyeStarfall@lemmy.blahaj.zone 1 point 8 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev -1 points 8 months ago

Maths is so much more malleable and abstract than what you think it is

No it isn't, as per Maths textbooks

You really do not understand maths as well as you think you do

says someone who doesn't understand it at all

just to be told “nope! That’s just how it is!” with no further thinking at all

Just as well I'm their teacher then, hey? 😂 I showed you the textbooks, and you refused to look at them

A lot of maths is chosen

Nope! Only the notation.

So long as there not being contradictions or paradoxes, the formulation of a form of math is valid

You mean so long as it obeys the laws of nature

Which is why you have different forms of maths with different rules

But we don't have different rules, only different notations. The rules of Maths are universal

And you really could use some more humility

says person who refuses to look in Maths textbooks

it’s obnoxious when you act all so high and mighty and arrogant,

says person who refuses to look in Maths textbooks

with no interest in questioning your assumptions

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.

Devolving into ridiculing the person you’re discussing with

Like the person who refuses to look in Maths textbooks

told clearly “I chose this.”?

No-one chose it. There are even several species of animals that know how to count! 😂 It's a universal law

You are making your arguments effectively unfalsifiable by just going “Nuh uh” all the time

Just as well I also provide the proof in the form of Maths textbooks. Oh wait, you keep refusing to look at them! 😂

Get some humility

says person who refuses to look in Maths textbooks

learn a bit about the foundations of maths.

says person who knows nothing about it. Makes up fanciful stories like it was "chosen" when nature proves otherwise

See for yourself what actually is the foundation

It's Arithmetic. Even some animals know how to do Arithmetic, none of them know how to do set theory! 😂

And, spoiler, it’s not a high school textbook.

That's right, it's a Primary school textbook 😂

Hopefully I do not need to tell you how concepts are simplified for younger students

And yet you still manage to not understand them 🙄

instead of overwhelming them with the complete knowledge of a subject

Welcome to why Algebra isn't taught until Year 7 😂

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[–] marcos@lemmy.world -1 points 9 months ago (1 child)

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.

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[–] SmartmanApps@programming.dev -1 points 8 months ago