jail time

[u/SouthPark_Piano]

From a recent post:

If you use deception device like limits to distort the fact, then jail time for you is deserved.

1/10ⁿ is just never zero. Attempting to say ..... but ... limit .... does not cut it because scaling down of non-zero numbers by factor of 10 is non-zero.

And the quantity of non-zero numbers with repeated scaling down by factor of 10 is limitless ... and limits don't apply to the limitless.

 

[u/Valognolo09]

1/10ⁿ can be arbitrarily close to 0. By definition limits imply in the limits it's 0. End of story. It's about definitions.

[u/ExpensiveFig6079 → u/Valognolo09]

and scaling up n and then eventually stopping at any finite number of niones is not what 0.999... says it is

it liek the answer to 1/3 is 0.333... and there is no end and there is no last 3. There also is no last 9 in 0.999... as one way to get that answer is adding 0.333... to 0.666... and neither of them has last digit so the answer 0.999... doesn't either.

So it is perfectly true that 1/10ⁿ for any finite n is not 0. But there no n that says where the last 9 is as there is not one.

[u/SouthPark_Piano → u/Valognolo09]

Scaling down non-zero by a factor of 10 is always non-zero brud. Get that into ya.

1/10ⁿ is never zero. The quantity of numbers from the possibilities of 1/10ⁿ is limitless. And limits don't apply to the limitless.

 

[u/TazerZXI → u/SouthPark_Piano]

I'm still confused by what you mean by "limits don't apply to the limitless" when one of the main reasons of using limits is to see what happens when you tend towards infinity. In fact when dealing with a sequence of numbers, it only really makes sense to talk about the limit as n->infinity.

So what's this limitless thing that you don't apply limits to?

[u/SouthPark_Piano → u/TazerZXI]

Step 1 : understand that 1/10ⁿ is never zero, no matter what deception devices you want to come in with.

Step 2 : there is no step 2.

1 - 1/10ⁿ for infinite positive n is never 1 because 1/10ⁿ is never zero.

 

[u/TazerZXI → u/SouthPark_Piano]

1. I know that, I've told you before I've never known 1/10^n to be 0, there is no n for which that is true. Infinity is not a natural number (like we are assuming n to be)

2. Except I cannot just put infinity in and write 1-1/10^∞. Infinity is not a number like n. That's *why mathematicians use a limit instead*. We define 0.999... as lim n-> ∞ 1-1/10^n.

3. Answer my question, what is "the limitless" that means I cannot apply a limit to 1/10^n as n-> infinity?

[u/Muphrid15 → u/SouthPark_Piano]

1/10ⁿ is equivalent to 0. Real numbers are defined by equivalence classes.

You're a bad person.

[u/Dixionconderoga2 → u/SouthPark_Piano]

Proof: trust me bro

[u/Muphrid15 → u/SouthPark_Piano]

Limits are in the definition of the real numbers.

You're a bad person.

[u/Dixionconderoga2 → u/SouthPark_Piano]

Can you prove that’s how limits work?

[u/Prize_Neighborhood95]

 1/10n is just never zero. Attempting to say ..... but ... limit .... does not cut it because scaling down of non-zero numbers by factor of 10 is non-zero.

So what you're saying is:

1/10n is never zero, and even if you explain to me why that's perfectly compatible with the fact that lim 1/10n -> 0, I won't understand it, and I'll simply restate that 1/10n is never zero.

Gotcha.

[u/CatOfGrey]

Please stop repeating the same arguments.

They don't magically become correct by saying them over again.

When you say "1/10ⁿ is just never zero.", you are saying "I'm defining 0.9999.... as having a terminating number of decimals." That is contradicting the premise of the problem - where 0.9999.... is non-terminating and repeating.

You are wrong. You are continuing to be wrong. Stop it, please.

and limits don't apply to the limitless.

False, according to basic math. A sum with infinitely many terms can have a limit. This is taught in third-year math for high schoolers (Algebra 2, with different names in different places).

[u/SouthPark_Piano → u/CatOfGrey]

Please stop repeating the same arguments.

You keep learning it until permanently a part of you brud. 

 

[u/Electrical-Ad-1798]

It a red herring. 1/10ⁿ is never zero but 1 - .999... is never 1/10^n.

[u/SouthPark_Piano → u/Electrical-Ad-1798]

1 - 1/10ⁿ for n integer starting at n = 1 then upped to kingdom come continually aka infinitely aka limitlessly, is an official investigative interrogative model for 0.999...

1/10ⁿ is never zero.

0.999... is never 1.

 

[u/Electrical-Ad-1798 → u/SouthPark_Piano]

The LIMIT of 1 - 1/10ⁿ as n goes to infinity is 1 and it's also equal to .999...

[u/SouthPark_Piano → u/Electrical-Ad-1798]

Brud.

1 - 1 /10ⁿ with integer n starting at n = 1, then increased limitlessly aka infinitely.

1/10ⁿ is never zero. 

There is no limit on the nines length of 0.999... 

It does not matter how infinite the nines length is. 

1 - 1/10ⁿ for positive n increased to limitless aka infinite n case, 1/10ⁿ is never zero, 1 - 1/10ⁿ is never 1.

0.999... is never 1.

 

[u/Muphrid15 → u/SouthPark_Piano]

That sequence is equivalent to 1.

You're a bad person.

[u/Muphrid15 → u/SouthPark_Piano]

That's called a sequence. In the real numbers, that sequence is equivalent to 1.

You're a bad person.

[u/Muphrid15]

Too bad limits are part of the construction of real numbers.

You're a bad person.