0.(9) ≠ 1

so we have two "0.(9)"
0.(9) -> 1 --- real 0.(9)
0.(9) = 1 --- Imaginary 0.(9)

>Not equals, only converges to one.
yes equals, because 0.(9) is the notation for the limit, not the sequence of partial sums.

*sobs*

Infinity is NaN and so is the infinitesimal also NaN. These are concepts, not numbers. Pi is a number, infinity is not a number. Pi has a seemingly infinite amount of non-repeating decimal places, but "infinity" itself is not a property of pi, because infinity is a concept and not a number, no more than than a Ford F150 is a number, or a plastic bag is a number. You do arithmetic on numbers, and using infinity in arithmetic leads to useless results, because infinity is not a number but instead a vague, undefined amount of something, much the same as trying yo determine the numerical value of "some" or "a lot".
1÷3 = 0.3••• this is true
3÷3 = 1.0 this is true
0.3••• × 3 = 1.0 this is true
0.3••• × 3 = 0.9••• this is not true

the idea that 0.3••• × 3 = 0.9••• extends from the FLAW of thinking "0.3•••" is related to "3" for the obvious reason that both numbers contain a 3 and we assume 33×3 = 99, 3×3 = 9, 0.3 × 3 = 0.9, so 0.3••• × 3 must also have a 9 in the answer.

0.333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 is NOT the same number as 0.3•••, and it is as truthfully as different as 1 is different from 2, meaning 0.3••• is a UNIQUE number that is confusingly written using established numbers.
It would be like instead of a number existing for 8, you were meant to write colon-three instead ":3" so that the number line would be
0 1 2 3 4 5 6 7 :3 9, and instead of ":3" being a combined character on your keyboard where 8 would be, there is no such combination and you're expected to manually write ":" and "3" individually everytime you wanted to use the number eight. Its dumb, and as dumb as writing 0.n•••, or 0.n..., or 0.(n) or whatever the fuck you do, which is where the extended decimal base-18 system comes into play to solve by ease of interpretation.

You only know how to use someone else's theories and stupidly prove them every time by any means.
But you do not want to think with your head.
You can not create something new yourself.

Our conversation is over.

In short 0.999••• doesnt equal 1 because (1÷3)×3 does not actually equal 0.999•••, but instead the equation is "([a unique number])×3 so that that the answer is 1"

I dont know what you're talking about retard. This is my theory one, and we weren't having a conversation either. So far as I could tell you were just shitting out brain diarrhea which no, that does not pass for information conversion much less conversation. Stay a forever brainlet.

0.9
0.99
0.999
0.999...9

Look, there are only nines here.
There is no one here.
0.999...9 - absolute limit.
The largest number of model.
After him there is nothing.
And this number itself is unattainable.

But you say that there is something after infinity.
You violate the laws of the model.
You are violating our old arrangements.

1,2,3,... -> infinity -> another reality
What kind of absurdity?
It is impossible to combine these models together.

An infinite number of points in a segment.
There are two incompatible realities.
0.(9) = 1 only in the world of segments, but not in the world of points, they do not even know about the existence of 1.

But you prove that they know about the existence of 1 and that their world must live according to the laws of your world.

>you ever smoked so much weed you became a foreigner?
honestly my guy, it is very difficult to understand you. What is your native language?

...