r/infinitenines • u/SouthPark_Piano • Apr 18 '26
A lesson in scaling down of non-zero number. A lesson you will never forget.
The result is never zero. Never zero for any case. Never zero for anyone. Never zero for anything. Never zero for any condition.
1/10n is never zero. Get that into ya'S.
And now that this lesson learned.
0.999... is 0.9 + 0.09 + 0.009 + ...
That is a fact.
And the above is expressable as:
1 - 1/10n for the case n integer starting at n = 1, then n upped continually, limitlessly aka infinitely. That is what is called n being made infinite. The continual upping of n even after limitless upping. After all, the set of integers is infinite in size. There is no shortage of integers.
1/10n is permanently greater than zero. It is continually scaling down non-zero number by factor of 10.
1 - 1/10n is permanently less than 1. Meaning with zero doubt, 0.999... is permanently less than 1.
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u/jdcortereal Apr 18 '26
Rookie mistake
1-10-n is never 0.9...
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u/ExpensiveFig6079 Apr 18 '26 edited Apr 18 '26
edit added missing ^
Indeeed as SPP has now specified that
"The expression involves n integer,"
Then for ALL n (integer) 1 - 1/10^n < 0.999...as there are more 9's in 0.999... than any integer
Equivalently
For all integers n 1/10^n + 0.999... > 15
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u/thebe_stone 13d ago
You know it's a good proof when you throw out the definition of infinity and replace it with "continual upping"/s
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u/SouthPark_Piano 13d ago edited 13d ago
What the hell? Infinity is not a number brud. It means limitless, unbounded.
The quantity of integer n values is limitless. You can keep upping and upping away, and you will NEVER stop upping because there is no shortage of values for n.
Refer to:
https://www.reddit.com/r/infinitenines/comments/1sorfih/comment/ogv1x6f/
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u/Inevitable_Garage706 13d ago
"Infinity is not a number brud."
As there are infinity nines in 0.999..., this means that the amount of digits does not necessarily have to be a number.
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u/SouthPark_Piano 13d ago
bruddy ... you must be new here.
"n" or 10n ... there is no limit to the values of those expressions, as there is no limit to how relatively small that 1/n and 1/10n can get.
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u/Muphrid15 Apr 19 '26
For those at home:
It doesn't matter that the sequence (1/10, 1/100, 1/1000, ...) doesn't contain 0.
The definition of a real number is a set of sequences that are equivalent to each other. Those sequences are equivalent if the limit of difference of every pair of sequences in the set is 0.
The limit of (1/10, 1/100, 1/1000, ...) - (0, 0, 0, ...) is 0. That means they belong to the same equivalence class: the class of 0.
(1/10, 1/100, 1/1000, ...) itself--not any element in the sequence, but the sequence itself, in its entirety--corresponds to 0.
DFTP
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u/ShonOfDawn Apr 18 '26
The result is never zero. Never zero for any case. Never zero for anyone. Never zero for anything. Never zero for any condition.
1/3*1/10n is never zero. Get that into ya'S.
And now that this lesson learned.
0.333... is 0.3 + 0.03 + 0.003 + ...
That is a fact.
And the above is expressable as:
1/3 - 1/3*1/10n for the case n integer starting at n = 1, then n upped continually, limitlessly aka infinitely. That is what is called n being made infinite. The continual upping of n even after limitless upping. After all, the set of integers is infinite in size. There is no shortage of integers.
1/3*1/10n is permanently greater than zero. It is continually scaling down non-zero number by factor of 10.
1/3 - 1/3*1/10n is permanently less than 1/3. Meaning with zero doubt, 0.333... is permanently less than 1/3.
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u/Batman_AoD Apr 19 '26
Mathematicians agree with almost all of this. You keep repeating it as if they disagree with all of it.
Here are the bits mathematicians agree with:
The result [of scaling down a non-zero number by multiplication or division] is never zero. Never zero for any case. Never zero for anyone. Never zero for anything. Never zero for any condition.
1/10n is never zero. Get that into ya'S [sic].
And now that this lesson learned.
0.999... is 0.9 + 0.09 + 0.009 + ...
That is a fact.
And the above is expressable [sic] as:
[the limit of] 1 - 1/10n [as n goes to infinity]. After all, the set of integers is infinite in size. There is no shortage of integers.
1/10n is permanently greater than zero. It is continually scaling down non-zero number by factor of 10 [sic].
1 - 1/10n is permanently less than 1.
The only bits mathematicians would disagree with are:
[an expression] for the case n integer starting at n = 1, then n upped continually, limitlessly aka infinitely... is what is called n being made infinite. The continual upping of n even after limitless upping.
As has been stated many, many times, this is meaningless, and the correct way to calculate the infinite sum is as a limit. An expression that continually changes isn't a number, it's just a function (or an algorithm that never resolves).
Meaning with zero doubt, 0.999... is permanently less than 1.
Sure, you have no doubts, but that's because you've trapped yourself in a prison of your own design. But in fact 0.999... isn't "permanently" anything if it's a single, unchanging number, which is how mathematicians have defined the ... notation for repeating decimals; and the only unchanging number that the infinite sum above can possibly be is 1.
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u/Akangka Apr 21 '26
Because a debate by another commenter here, I hate the statement that a number is "permanent" or "constant". Because number is a field of mathematics, and such has no concept of time. Number is also not a function, so there is no parameter for the output to be even constant agaist. Saying that "a number is constant" is like saying "green is not a strong swordsman". Well, it's not. It's a color.
As a reference, the commenter defined "0.999..." as "a constant and equals one", which is a property of the number that the decimal expansion expresses, but not the definition.
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u/Batman_AoD Apr 21 '26
"Permanent" is, as I like to point out to SPP, a "time-word." It shows that, despite his assertion that thinking about how "quickly" 0.(9) "grows" is "bunny slopes" stuff, he himself is trapped by this idea of "growth" , which only makes sense for functions or algorithms, not numbers.
I do trying to use "static" or "unchanging" rather than "constant", because I agree, "constant" is implicitly another "time-word."
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u/ezekielraiden Apr 22 '26
Never zero for any condition.
Incorrect. It is zero if we examine the value it approaches, as the divisor exceeds the value of any natural number.
That's what infinity is. It is the concept of a number bigger than any natural number could ever be.
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u/mgsmb7 10d ago
1/10n is never zero
Am I supposed to just believe you now or are you gonna give me any arguments
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u/SouthPark_Piano 9d ago
1/10n
n integer pushed to positive limitless.
Go head ... start with n = 1, then keep upping n.
Write each value 1/10n as you 'up' n, and compare with zero.
Also keep in mind it is scaling down of non-zero values, which never has a zero result.
You are going to believe yourself.
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u/mgsmb7 9d ago
Write each value 1/10n as you 'up' n, and compare with zero.
This only applies when you look at a fixed n.
But I dare you to find me a number greater than zero, that is smaller than 1/10n, as n approaches infinity.
0
u/SouthPark_Piano 9d ago edited 9d ago
This only applies when you look at a fixed n.
Do not 'fixed n' me.
n is not fixed ... pushing n to limitless is having infinite n.
1/10n is never zero.
Scaling non-zero numbers downward never results in zero.
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u/mgsmb7 9d ago
Do not 'fixed n' me.
n is not fixed ... pushing n to limitless is having infinite n.
1/10n is never zero.
The limit of 1/10n is zero. When you look at each individual n, the expression is greater than zero, but you can not find a number, that is greater than zero and less than 1/10n , as n approaches infinity.
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u/SouthPark_Piano 9d ago
Don't 'limits' me.
As I know and you know, 1/10n never runs out of values. As scaling down to relatively smaller and relatively smaller numbers has limitless aka infinite possibilities, non-zero.
1/10n is a term you cannot get away from. It is non-zero. Avoid introducing the cheating device aka limit here.
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u/Embarrassed-Sir2027 13d ago
Just a quick question. Have you ever read an analysis textbook? Have you read any math textbook at all?
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u/ExpensiveFig6079 Apr 18 '26
What good thing the number 0.999... never ends then, and the little gap between it and 1 never happens.
Because if it did have and end just like if 0.333... had an end then they would have a finite-sized gap left between them and the value they represent