r/limitlessnines

This video is worth a watch

u/TamponBazooka defines 0.9... as the biggest number smaller than 1.

This must also imply that there is a smallest number bigger than 1 lets call it ψ. This can be constructed by subtracting 0.9... from 2.

ψ = 2 - 0.9... > 1

Now my question to anyone willing to participate is, how do we write this number? Surely there is a simpler form than a term with two numbers.

You might think we should just write it as 1.0...1, but u/TamponBazooka has previously stated that something like 0.9...5 is ridiculous and does not exist, so I would assume 1.0...1 also doesn't exist.

Additional numbers where representations should be found:

smallest number bigger than 0, constructable by ψ - 1

biggest number smaller than 0, constructable by 0.9... - 1

I already explained it a few times. So far nobody could bring a good counter argument. So maby we can use this post here to discuss!

0.(9) is permanently less than 1

0.(3) is permanently less than ⅓

Keep writing 0.333333333333333333333333333

and it never reaches ⅓

This post isn't intended to prove that 0.999... = 1, but it is intended to show why one of SPP's favored arguments, the "lack of a limbo kicker", isn't actually convincing to anyone who disagrees with him.

In the quoted post, SPP phrases the argument as "you need to add just the right touch of a limbo 1 to generate a 1 from the summation 0.999...9 + 0.000...1."

This is obviously true if the "..." in 0.999...9 indicates a large-but-finite number of 9s. That is, 1 - 0.999...9 = 0.000...1, where the number of 0's between "." and "1" is one less than the number of 9's.

But, [Morpheus voice] what if I told you that the "right touch of a limbo 1" is this number: 0.000...0999...?

There's obviously an ambiguity of notation here, because the first "..." is finite but arbitrarily large, whereas the second is actually infinite. So let's adopt the notation proposed by u/Inevitable_Garage706 in this post: (0_n) means n 0's for some large n, and (9_∞) means infinite 9's.

I am not going to prove here that 0.(0_n)(9_∞) is equal to 0.(0_n-1)1. But I will point out that they are equal if and only if 0.999... = 1, and for the same reasons. So, for anyone who accepts that standard equality, then there is indeed a unique "limbo kicker" for every 0.(9_n) that is already part of 0.(9_∞). Because for any n, 1 = 0.(9_n) + 0.(0_n-1)1 (this is SPP's "limbo kicker"); and it is also the case that 0.(9_∞) = 0.(9_n) + 0.(0_n)(9_∞). (Note that here SPP may object that it's actually 0.(0_n)(9_∞-n), but those are only different if ∞ is some kind of finite-but-increasing value, or a transfinite ordinal.) So, for someone who believes (i.e. sees why) 0.(9_∞)=1, it's easy to see that:

0.(9_∞) = 0.(9_n) + 0.(0_n)(9_∞) = 0.(9_n) + 0.(0_n-1)1 = 1

...because the limbo kicker was always inherent in 0.(9_∞) itself.

https://www.reddit.com/r/mathematics/s/ZhEG7xtHvG

I genuinely believe that SPP is just incredibly misinformed and deadset in their ways, but they don't really have any real malicious intention. Even Just_Rational_Being/French_Slumber, snarky as he is, does seem to genuinely believe in finitism, even if he has to use AI slop to prove it.

TamponBazooka is completely different and that's why I have to specifically call her out. Not to make her a target of harrassment, but because she's a toxic troll, full stop. She doesn't believe in anything she says, she only says whatever she thinks ragebaits the other person the most. That's my main problem with her. She's not even the type of troll that wants to have fun, she's just here to deliberately make everyone angry.

I have to call her out because it's making the main sub a horrible place to talk in. SPP is fun and nice, at least. She isn't.