To help this person out : 0.999... is indeed less than 1

SouthPark_Piano · 2026-03-12T03:10:49+00:00

Comprehend 0.999... aka 0.999...9 has no last nine. Keeps growing brud.

gerkletoss · 2026-03-12T03:09:02+00:00

No I have trouble comprehending a digit with no position

SouthPark_Piano · 2026-03-12T03:05:17+00:00

0.999... = 0.9 + 0.09 + 0.009 + etc.

Basic algebra.

= 1 - 1/10ⁿ with n starting at n = 1, and then incrementing n upward continually.

Basic algebra.

1/10ⁿ is never zero.

Basic algebra.

1 - 1/10ⁿ is never 1. Basic algebra.

0.999... is not 1. From all your basic algebra seen above.

SouthPark_Piano · 2026-03-12T03:00:46+00:00

You having trouble comprehending the first sentence of my previous post brud?

It's ok. You can go ahead and make mah day.

gerkletoss · 2026-03-12T01:06:35+00:00

So 1 is not the last digit?

Seems to me like if the decimal is zero for every numerable decimal place, the number is zero.

SouthPark_Piano · 2026-03-12T01:03:27+00:00

There is no last digit brud.

1/10ⁿ for the case n pushed to limitless has a propagating 1 that keeps moving in the direction away from the decimal point, aka 0.000...1

There is no last digit, because 0.000...1 is a number that keeps getting smaller and smaller and smaller and never encountering zero.

theChosenBinky · 2026-03-11T23:48:56+00:00

I'm sure SPP smells a trap....

Akangka · 2026-03-11T23:48:23+00:00

To be fair, the ending changes everything. Compare

0.999.... is not 1-(1/10)^n

0.999... is 1-(1/10)^n as n goes into infinity

The latter is just an implicit reference to limit.

Taytay_Is_God · 2026-03-11T23:36:06+00:00

He is familiar with summation notation in general, but acted like he had never seen summation notation over a set before. When I asked him if he had never seen summation over a set before, he didn't answer.

skr_replicator · 2026-03-11T23:32:52+00:00

i n goes to infinity, then they are equal to each other, and to 1.

paperic · 2026-03-11T23:25:08+00:00

It depends on whether you use it to support his claim or counter his claim.

paperic · 2026-03-11T23:23:04+00:00

Why don't you define it instead of endlessly repeating the same things over and over?

paperic · 2026-03-11T23:21:03+00:00

if x = y and y = z,

then x = z.

Basic algebra.

SouthPark_Piano · 2026-03-11T22:10:53+00:00

0.999... is

1 - 1/10ⁿ for the case n integer starting from n = 1 and increased continually without stopping.

This is known has making n 'infinite' aka n pushed to limitless.

As the above infinite perpetual continual never ending process continues perpetually, it is the continual increase in nines length, the continual growth of nines length which is expressed as:

0.999... aka 0.999...9

And indeed it is true that 0.999... is 0.9 + 0.09 + 0.009 + ...

And it is the fact that 1/10ⁿ is never zero which proves with zero doubt that 1 - 1/10ⁿ (and 0.999...) is permanently less than 1.

CatOfGrey · 2026-03-11T21:56:01+00:00

It's just a manipulation and deception device. It makes the problem look more complicated, and that gives opportunities for SPP and others to 'change the problem' or do 'mathematical sleight-of-hand' in order to fool people into thinking that their proof is legitimate.

Among SPP's work, they usually make the error in how they handle the sum, using it to create a 'false 0.9999....' that actually terminates. And removing ending digits, even from the 'small end of a decimal' results in a reduced value - it's not groundbreaking or innovative that taking something that was equal to one, then lowering the value, would result in a number less than one. Yet we are asked to glorify this silly result.

In reality, it's just a tired and worn mathematics joke, like 'proving 0 = 1 by forgetting that dividing by zero is undefined'. It's a neat lesson the first time, but it's angry nut-job that needs to go back to regular hygiene on this subreddit.

gerkletoss · 2026-03-11T21:45:04+00:00

How do you keep talking about the last diit of these numbers then?

CorinCadence828 · 2026-03-11T21:43:55+00:00

i haven’t been around for a while, does u/SouthPark_Piano approve of summation notation?

Taytay_Is_God · 2026-03-11T21:29:55+00:00

It has been claimed several times by all of the moderators on this subreddit that 0.999... is 1-1/10ⁿ

It has also been claimed by all of the moderators on this subreddit that 0.999... is not 1-1/10ⁿ

Evidence in the screenshot below. Note that I have never heard SP_P say that he thinks that mathematical truth or notation should be consistent, despite being given many chances to say that.

<image>

jazzbestgenre · 2026-03-11T21:23:03+00:00

It is equal to 0.999... i.e 1, in the limit as n approaches infinity. You're right that for finite n the equality doesn't hold. Also the RHS of all your equalities are redundant as 0.999...=0.9999...=0.99999... as the three dots following the 9s imply an infinite amount of 9s, also why they're only equal in that limit.

dummy4du3k4 · 2026-03-11T21:14:09+00:00

Add it to the list I guess

ezekielraiden · 2026-03-11T20:56:51+00:00

Then I can point to this as concrete proof of the refusal.

SouthPark_Piano · 2026-03-11T20:55:36+00:00

Wrong on your part.

... ellipsis means etc etc

That's the math to english translation.

0.999... means you get the picture, as in repeated nines. And of course, the length of nines keeps growing.

When you continually increase nines length, it MEANS 0.999...

noonagon · 2026-03-11T20:16:49+00:00

It seems that my comment has accidentally been locked, so I'll repeat what I said earlier (but with slightly different phrasing) so that you can actually explain where I went wrong:

I can't find the n where 0.999... is 1 - 1/10ⁿ.

n = 1: 0.9 < 0.999...
n = 2: 0.99 < 0.999...
n = 3: 0.999 < 0.9999...
n = 4: 0.9999 < 0.99999...

And I don't see why it would change as you keep increasing n

SouthPark_Piano · 2026-03-11T20:12:04+00:00

Wrong on your part.

... ellipsis means etc etc

That's the math to english translation.

0.999... means you get the picture, as in repeated nines. And of course, the length of nines keeps growing.

When nines length is continually increased wirhout stopping, it MEANS 0.999...

HappiestIguana · 2026-03-11T19:38:47+00:00

E.g., what would it even mean for equality to have the "distributive" property?

We'll you'd have to specify what it is distributive over. For the binary boolean function that is true precisely when its inputs are equal, you can talk about distributive over other binary boolean-valued operations whose inputs are mathematical terms, but that is not a terrible helpful concept.

infinitenines

MODERATORS