Very important question

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I see what you're getting at but I think the issue is that 1.0000....1 isn't well defined in the sense that it doesn't actually exist

This is pretty trivial.

1.000...1 is not a real number, therefore there can't be any equality relation between it and any real number such as 1.

Just like 5.3 can't be equal to say 4 as one is a natural and the other clearly is not so what the fuck are you even asking?

Its not well defined

Heres a blog post about them from some math teacher
mathwithbaddrawings.com/2013/08/13/the-kaufman-decimals/

2.000... - 0.999... = 1.000... 1

I guess if that's how you want to define it then yes it would equal 1

shitposting

you are defining subtraction to retain some quantity based on the original series?

this is false as you would have indeterminite form. it's like when you divide by zero and approach the function from either side. it could be positive or negative infinity. yours is not actually properly terminating to ...1 when you take into account that 999.. never ends. therefore it can't work. how did you not realize this?

>1.000...1 is an indeterminate form
>Even though you can clearly define it as 1.000...1
Maybe human understanding of math is limited because our studies are brief and biased, and 1.000...1 is actually perfectly fine

How did this m.nnnnnnnnnnnnn+1 meme even start? I don't get it.

Ive said it before on other boards for like over a year but never in sci so I dont know.

Im not a math major and it seemed to trigger them and it can make sense on the surface so I brought it up always in the .999... = 1 discussions

-1 + 0.999... = -0

>-0

I happen to no the factual answer to this question, but I've left it deliberately obscured. Good luck.

This is correct, though retarded

It's 1

Wrong.

it's interdeterminate. depends on which infinity is "stronger"

Fuck you

>1 to the power of anything isn't 1
kek

>1

lim (1+1/r)^r=e
(r->oo)

Thats not 1^n

Hey everyone.

Wait til OP here's that 1.000..... = 1.000....1.

His mind is gonna be blown.

>He doesn't know about negative 0
Nobody tell him.

that equals 0 you imbecile

But does 1.000... = 1?
This is very important

>1.000...1 is actually perfectly fine
Subtract 1 from it in order to play around with the remaining infinitesimal 0.000...1
Divide it by 2, and you're given the infinitesimal 0.000...5
Better yet, multiply the original by 5 to get 0.000...5

You're left with the obvious, awkward result where 0.000...1 > 0.000...5, and that 0.000...5 =! 0.000...5
If you can find a way to make this rigorous, then it would be awesome. As it is, either the notation or the assumptions going into it don't work.

What are you on and where do I get some?

2 - 0.9999... = 1.

There is no such thing as 1.000...1

>1 divided by 2 = 5
You might want to check that
0.000...1 / 2 is clearly 0.000...05
If you divided it enough, you'd eventually get to 0.000...000...1

>subtract 1 from it
you then have zero.

that's like saying 0.999... - 1 is -0.00...1 kill yourself

>that's like saying 0.999... - 1 is -0.00...1
But 0.999... is 1, so 0.999... - 1 is negative zero. We're talking about 1.000...1 here, which is different.

no u
You either misunderstand what I'm saying, or are trying to say that 1.000...1 =! 1, but that 0.000...1 = 0. I'm assuming the babby's first math in this thread and playing with it, trying to show that it doesn't work.

So any finite number of divisions adds a finite number of 0s to the current level of infinitesimalness, but an infinite (or just eventual) number of divisions drop it to a smaller kind of almost-nothing.

If that is repeated infinitely, will the infinitesimal reach 0, or is 0.000...000...000...etc somehow distinct?

>If that is repeated infinitely, will the infinitesimal reach 0, or is 0.000...000...000...etc somehow distinct?
It's distinct, you can tell because 0.000...000...000...1 is very small.
As a scientist, I can tell you that this is very useful when calculating inverse distance, for example a really small number like 0.000...000...1 would be really far away. Trust me on this.

The examples brought here are still finite versions of this which isn't what I'm asking about.

(0.000...1)^2 = 0.000...000...1
So the question is whether or not lim n->inf (0.000...1)^n = 0, for which the answer is no. It's ellipses all the way down. Perhaps a new notation is warranted after all.

Just like imaginary numbers don't exist, right?

To propose a new notation,[...] should be used in cases like this. For example, the limit of that equation would be 0.000...[...]...1

Great, then that can be expanded to 0.000...([...]^(n))...1 in cases of really small numbers.

what the fuck are you smoking. Even if we ignore the obvious error in even trying to define something like "0.000...01" (if you mean finitely many zeros, use scientific, if you mean infinitely many it makes no sense to add a digit at the end), what you've desperately attempted to claim is a reasonable number is strictly less than 1. For ANY number strictly less than 1 (in magnitude), [math]
0\le a< 1\implies \lim_{n\to \infty} a^n =0
[/math]. You've wiggled into a corner where either now you admit you've no idea what the fuck you're on about (true) or somehow these ill-posed ellipses produce a number GREATER than 1 in magnitude when added to some decimal expression (nonsense).

Your problem is that you are creating finite number with infinite decimal integers, which is impossible.

>a reasonable number is strictly less than 1
All numbers are reasonable
The problem with your thinking is that this math is very high-level.
The idea that [math]0≤a

1.000...
is impossible then, oh thank you guru for sharing your pearls of wisdom

see
We're all doing our part to answer whether or not that is the case. Please don't be rude

1.000... is possible though. Infinite decimals.
1.000...1 is not because the 1 at the end of the infinite string of zeroes makes the number finite.

looking back, your earlier posts were even more obvious. carry on shitposting, m8. Nothing else on this shitty board. You might want to reword
>understands that numbers which approach zero never truly reach zero
as that literally translates to 'I'm ignoring all the results of analysis' since its a red flag that you misunderstand (or rather, are intentionally misusing) the notion of a limit.

At least get some better webms to distract from the nonsense in the thread.