10x = 0.999… + 9 (true by algebraic manipulation)

No, you haven’t shown that, because you haven’t shown yet that 9x=9. Welcome to why this doesn’t prove anything. You’re presuming your result, then using it to “prove” your result.

What we know is that the right hand side is 10 times 0.9999…, so if you want to substitute x=0.99999… into the right hand side, then the right hand side becomes 10x (or 9x+x)… which only shows what we already know - 10x=10x. Welcome to the circularity of what you’re trying to achieve. You can’t use something you haven’t yet proven, to prove something you haven’t yet proven.

According to me, talking about the origin of the 0.999…

Right. So not according to the meme, which doesn’t tell us where the 0.999… comes from. Nor the 1 - could be an integer, floating point, or an estimation. Thanks for playing.

And if you don’t then you can no longer claim they are still equal.

you can substitute anywhere

And if you are rearranging algebra you have to do the exact same thing on both sides, always

This isn’t about limits of accuracy

According to who? Where does it say what it’s about? It doesn’t.

please show me how basic arithmetic can make 0.999

You still haven’t shown why you’re limiting yourself to basic arithmetic. There isn’t anything at all in the meme to indicate it’s about basic arithmetic only. It’s just some Maths statements with no context given.

then a correct use of the system must be applicable to everything, right?

Different systems for different applications. Sometimes multiple systems for one problem (e.g. proofs).

You shouldn’t need a new system like algebra to be correct, right?

Limits of accuracy isn’t algebra.

not taught yet

What do you mean not taught yet? There’s nothing in the meme to indicate this is a primary school problem. In fact it explicitly has a picture of an adult, so high school Maths is absolutely on the table.

There is no method by which basic arithmetic and decimal notation can turn 0.999… into 1.

In high school we teach that they are the same thing. i.e. limits of accuracy, 1 isn’t the same thing as 1.000…, but rather 1+/- some limit of accuracy (usually 1/2). Of course in programming it matters if you’re talking about an integer 1 or a floating point 1.

If someone uses these systems as they were taught, they will get told they’re wrong for doing so

The only people I’ve seen get things wrong is people not using the systems correctly (such as the alleged “proof” in this thread, which broke several rules of Maths and as such didn’t prove anything), and it’s a teacher’s job to point out how to use them correctly.

P.S.

“We do it like that, therefore, it is right”

Yep, Maths teachers do it right. :-)

You’re just another yank

BWAHAHAHA! I see you still didn’t learn to check facts first. 😂😂😂

X times 10 is 10x

10x is 9.9999999…

As I said, they didn’t substitute on both sides, only one, thus breaking the rules around rearranging algebra. Anything you do to one side you have to do to the other.

P.S. you proved my point

The only people who think there’s something wrong with PEMDAS are people who have forgotten one or more rules of Maths.

https://www.youtube.com/watch?v=lLCDca6dYpA

…oh wait I remember that

Well, you seem to have forgotten that the woman in that video isn’t a Maths teacher, which would explain why she’s forgotten the rules of The Distributive Law and Terms.

until you gave up

I didn’t give up, you did.

I suggest we don’t do it again but instead, you review the thread

I suggest you check some Maths textbooks, instead of listening to a Physics major.

those systems are giving an incorrect answer

When there’s an incorrect answer it’s because the user has made a mistake.

Instead of telling those people they’re wrong

They were wrong, and I told them where they went wrong (did something to one side of the equation and not the other).

Maths teachers are constantly wrong about everything

Very rarely wrong actually.

the abomination that is PEMDAS

The only people who think there’s something wrong with PEMDAS are people who have forgotten one or more rules of Maths.

you can prove it with math

Not a proof, just wrong. In the “(substitute 0.9999… = x)” step, it was only done to one side, not both (the left side would’ve become 9.99999), therefore wrong.

Who’s on first? :-)

1/2x is also unambiguous. 2a=(2xa) by definition. Has done for at least 180 years. Terms

Nothing wrong with the way it’s written - division before subtraction.

Just make sure you don’t use an e-calculator, nor a Texas Instruments calculator.

Within those three groups it doesn’t really matter which ones you do first

It absolutely does matter. You must do exponents after brackets and before multiplication and division, for the precise reason you said that exponents are shorthand for multiplication. In other words, there’s 4 groups, not three.

They’re all correct, since the mnemonics are just ways to remember the actual rules