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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

@ SmartmanApps @programming.dev

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8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago
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...
Isn’t that interesting?
No, all of it was wrong, again 😂

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

You must not distribute brother

Literally a Law of Maths, but go ahead and stay in Denial about it 😂

It’s optional

You think the word "must" means it's optional?? 😂

Google distributive law and find me one source saying it’s imperative to distribute

Go through Maths textbooks and find me one which says it isn't, or alternatively go through dictionaries and find me one that says "must" means "optional" 😂

there’s none

He says, when I've already posted multiple textbooks which say it is 😂

You can even confirm this is true yourself with simple examples like the ones I’ve mentioned above

I've confirmed it with Maths textbooks - you know, those things you refuse to look in because you know they prove you are wrong 😂 BTW your "example above" was about The Distributive Property, as I already pointed out to you at the time

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

you’re just using (AS) without realizing it

as per the 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 🙄

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Believe what you like.

Same as all Mathematicians, textbooks and proofs.

Including that all mathematics communication and education is flawless and incapable of any ambiguity, apparently

Yep

made you decide that insulting my intelligence was the best way to have this conversation

you were the one who decided to refuse to look in Maths textbooks 🙄

Actual math educators, on the other hand, are moving away from using the “PEMDAS” (or “BEDMAS”) acronyms

No they aren't.

because of the ambiguity inherent in them

There isn't any ambiguity in them 🙄

using “GEMS” (or “GEMA”) instead

Nope. No Maths textbooks are using that.

the acronym must not be all that useful.

And if that is true, then GEMA would be completely useless 🙄

You’re trying to make me mad,

No I'm not.

Again–have a good one

Again, you still couldn't provide a shred of evidence to support your argument

8mo ago

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128

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Here is math for kids

Yep, that's about The Distributive Property too 🙄 Every time Multiplication gets mentioned, you know they're talking about the Property, since the Law has no multiplication in it, but The Distributive Property of Multiplication over Addition does

Distributive law means you are allowed to distribute

No, the Property does. The Law tells you that you literally must Distribute.

not that you must distribute

Because The Law says that, hence why it's a Law 🙄

I’m so sorry for the amount of effort you’re futilely putting into this lmao

says someone who can't even tell the difference between the Property and the Law 😂

Nowhere in all your sources and screenshots is it stated you must distribute

Yes it does liar

thus the entire argument breaks down

Not for people who know how to read 😂

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

That time I didn’t use the term implied multiplication I merely said that the multiplication is implied

And there's no such thing as either 🙄

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

And what do you do with and and the b and then the a and the c? If you want to simplify the equation?

Add them, obviously 🙄

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

And what do you do with the number inside the when you want to get rid of it?

You literally must distribute the coefficient before you can do anything with what is inside to remove Brackets, as per The Distributive Law, a(b+c)=(ab+ac), now you can work on getting rid of what is inside.

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Open a textbook

I've been telling you to do that the whole time and you still refuse 😂

Tell them, not me

Tell them you refuse to open a Maths textbook? 😂

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

I don’t take homework from insufferably smug jerks on the Internet

Nor Maths teachers apparently, which would explain a lot. Hilarious that you say goodbye when you can't back up what you said with a single example

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Yes it is

You can say that as much as you want and you'll still be just as wrong. Noted that, yet again, you are unable to cite any Maths textbooks that agree with you

If you understand what is multiplication and what is addition

Again, the mnemonics are for people who don't understand, which would be people like you! 😂

What’s the result of 2/2 and what’s the result of 2*½

What's the result of 2+2? What's the result of 1+3? Are 2+2 and 1+3 the same? No! 😂 2 apples + 2 oranges = 4 pieces of fruit. 3 apples and 1 orange = 4 pieces of fruit. Is 2 apples and 2 oranges the same as 3 apples and 1 orange? 😂 Anything else you want to embarrass yourself about not understanding?

Explain how is that relevant to the discussion

You're the one who brought it into the conversation - you tell me! 😂

where brackets are only used for readability sake

You'll find most people find that less readable. Welcome to why textbooks never use them

they’re not changing the results in any way

Just making it less readable.

Well… yes, because we’re not talking about the history

You are when you start dragging brackets into something that never used brackets for hundreds of years

we’re talking about the current rules

which haven't changed at all in all that time 😂 2-3 has never and still does not require brackets, same as when Arithmetic was first written.

This whole thread stemmed from the fact that some people were taught PEMDAS while others where taught PEDMAS.

and everyone was taught that the order of DM/MD does not matter. If it did then one of them would not exist

Are you suggesting that the order of operations depends on your maths teacher?

No! You might want to work on your comprehension as well 😂

Wow, let me be the first to welcome you to the Internet!

Been here longer than you probably, and know full well what you said is a lie 😂

Now find one that actually talks about that

Already posted a screenshot of one. You really need to work on your comprehension

the addition of similar monomials, which is a different thing altogether

Set all the pronumerals to 1, and guess what you have - the exact same thing 😂 I see you don't understand how pronumerals work either

BTW you still have not cited any textbook whatsoever that agrees with anything that you have said, in case you needed that reminder 😂

instead just read the part you posted, but slower.

says person who doesn't understand that pronumerals can equal 1. 🙄

the arithmetical difference between the total of the positive and the total of the negative coefficients,

Yep, 1a-2a+3a-4a=a((1+3)-(2+4)). Now set a=1 and guess what you have? 😂

giving it the sign of the numerically greater total, and annexing it to the common literal part

You telling me you don't understand what that means? +4-2=+2. +2-4=-2. Not complicated

Which actually

proves you're wrong 😂

Addition is NOT first

You know the textbook just literally told you it is, right?? 😂

unless it’s the first on the right

It's first regardless of where it is. Did the textbook says it depends on where it is? No 😂

Again, let me extend a warm welcome on behalf of everyone on the Internet

Where nearly half of adults have forgotten the rules of Maths, and everyone else knows there is no problem 😂

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Nowhere in your “proof” screenshots does it say anything about distribution being part of the brackets step

Which step is first? Brackets. What do they do first in 5(36)/9? The Brackets.

What does the other textbook do with bc? Puts it in Brackets. Which step is first in order of operations? Brackets 🙄 What do they end that page with? “those who study algebra are required to make their calculations conform to these laws”. You seriously need to work on your comprehension that I need to explicitly spell out to you what the textbooks say

Distribution is a method that can help solve equations

The Property is. The Law is a rule which literally must be obeyed, when solving expressions, as per Maths textbooks 🙄

it isn’t required

Yes it is! That's why it's a Law 😂

If you have 2(3+5) you’re free to solve it as 23+25 or as 2*8

Nope, neither

1/2(3+5)=1/(6+10)

1/2x3+2x5=3/2+10 WRONG ANSWER

1/2x8=8/2=4 WRONG ANSWER

Welcome to why it must be in brackets, as per Maths textbooks 🙄

That is because juxtaposition means multiplication and nothing else

says person who can't cite any Maths textbook that says that. Nope! It means it's a Term/Product, the result of a Multiplication (or Factorisation), and nothing else...

Note that it never used the word Multiplication at all in that definition 🙄

Math textbooks almost universally will either use clear brackets or simply write divisions in 2 lines

or an obelus or slash on one line

which avoids the confusion altogether

Only people who don't remember the rules of Maths are confused about it. Students have no trouble with it.

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo 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 😂

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

What do you mean? I replied to it…

Where you, yet again, ignored that I told you what you said is wrong, as per Maths textbooks

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Yes, it is

No it isn't 😂

Quote the part where I said you didn’t.

The part where you said to leave it out of the mnemonic "It should be limited - like Orders - to only Multiplication and Addition"

They are the same.

Nope. 2/2 is not the same as 2*½. Do you need glasses or something??

How is that “having it the wrong way around”?

Because 2-2 came first, before we started using Brackets in Maths, by several hundred years

What does that have to do with the topic at hand?

You glibly ignoring the history and rules of Maths 🙄

No, they’re not

Still wrong 😂

Mnemonic without understanding what you’re doing

That's EXACTLY what the mnemonics are for! 😂 Don't need to understand it, just follow the steps

Which is why people get confused and argue online that you must do addition before subtraction

No-one gets confused or angry about that. 😂 There are textbooks that specifically teach to do it that way

or the other way around, depending on what the mnemonic they learned was

I have never seen any textbook say to do Subtraction before Addition, everyone is taught Addition first

Understanding that subtraction is just the addition of a negative number solves this problem

Understanding that you can do them in any order proves there is no problem 😂

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

Yes, the math textbook says exactly what I said, that it’s a multiplication

Nope, they say it's Brackets...

5(36)=(5x36) <== Brackets

bc=(3x4) <== Brackets

There’s no mention of it being a separate operation taking precedence

It's part of the Brackets step. I have no idea what "separate operation" you're talking about

The parentheses in your example are added for clarity

Nope. They are there because The Distributive Law requires them. "those who study algebra are required to make their calculations conform to these laws".

Whether you give priority to juxtapositions is a

A literal Law of Maths. See textbook.

the consensus being to just use parenthesis around when writing in a single line to avoid confusion.

No it isn't. You won't find any Maths textbook that says that.

However, there is no distribution step taking precedence

There is the Brackets step, including Distribution, taking precedence, as per Maths textbooks 🙄

as you mentioned

As the textbooks mention

the whole debate centers around whether the writer was too lazy to add parenthesis

The only debate is by people like you ignoring what is taught in Maths textbooks.

8mo ago

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @programming.dev 8mo ago

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.