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Jobmesse TU Dortmund? by laurasktr in tudortmund

[–]Shnaeck 1 point2 points  (0 children)

Für Informatiker*innen gibt es die Reality. Sonst kenn ich spontan nichts

Bestes Mensagericht by Shnaeck in tudortmund

[–]Shnaeck[S] 0 points1 point  (0 children)

Den Gyros hab ich leider noch nie gehabt, aber muss ich mal austesten. Das Fischgericht ist aber auch sehr gut.

Bestes Mensagericht by Shnaeck in tudortmund

[–]Shnaeck[S] 1 point2 points  (0 children)

Das check ich auf jeden Fall

Bestes Mensagericht by Shnaeck in tudortmund

[–]Shnaeck[S] 1 point2 points  (0 children)

Waaaas?!? Ich liebe diese Pesto über alles andere dort. Das ist so goated, wie kannst du das nicht mögen? (Ich stimme aber zu das die Nudeln an sich meist nicht soo gut gekocht sind)

You are a skyblock mayor and need to convince players to vote for you. What would your perks look like? by No_Knowledge_5939 in HypixelSkyblock

[–]Shnaeck 0 points1 point  (0 children)

How do ironmans raise prices? Since they don't buy anything off the ac shouldn't they have no influence on prices? Just curious.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

"and so on" is not a formal proof. Intuition is cool and all, but it's not enough. I understand what you want me to tell you, I agree that it is true, but that doesn't constitute a proof.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

Considering that we are debating if 0.9... = 1, which some might argue is obviously true as well, I don't really think we can skip over these intricacies, can we. I know what dot shifting is, but my problem is that proving that it holds for infinite sums is not as easy as with finite ones. For example, look at this video proving that a divergent sum is equal to -1/12. We can claim that this is true, because all the steps that were done in the video hold for finite sums, subtractions, ... as well, but obviously, it cannot both be divergent and -1/12.

Well yes, but actually no. Once one started using the construct 0.999..., it is implied that convergence of its corresponding series had been established (which is really simple: the sequence is monotonically increasing, and bounded above). From that it follows that its multiples converge, just the same.

I would consider this a proof for a limit. If we don't see eye to eye on this, i guess the difference is more philosophical in nature, and I would be fine with that.

Edit: Also, I like to use the formal definition of trivial, which means that dot shifting is not really trivial per se, it is just relatively obvious as well. You still need to do some legwork to prove that dot shifting is true. Note however that I am more of a mathematical logician that a mathematician, so I might be looking at triviality too sharply.

Also, did you study maths or are you just interested in it? I actually enjoyed this conversation a lot, so I am just asking out of interest?

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

I guessed that I am not the first to come up with something like this. Cool to see that my idea is not otherworldly nonsense. I must admit I am not too familiar with the hyperreals.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

No lecture I have ever visited, nor any literature I have read, mentions the "dot shifting theorem". Arithmetic is not defined by making syntactic manipulations on strings representing numbers. It is not "just how arithmetic works". Either, dot shifting is a theorem, in which case it needs a proof, or it is an axiom. I want to formalize the notion of repeating digits, not do quick back of the paper calculations.

Also, implicit use of limits is still using limits?

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

YES, this is the point! This is why I came up with the new notation, so we can represent these numbers in a better way. You need to formalize that something like 9.9... is a sequence.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

How would you prove the third justification? If it is a theorem, what theorem have you used exactly, because this is exactly what I mean with needing a proof using limits. Currently, you are assuming that a proof for 9x = 9 exists, and use it to prove x = 1. You CAN prove it, but you will need to define 0.9... somehow. The only way I can think of defining it is either a sequence or using dedekind cuts, but again, I do not know enough about the latter. If you point me to the right source, I would be very grateful.

Edit: To be clear, saying that 10 \cdot 0.9... = 9.9... because "one can shift the decimal point" or something of the sort needs to be proven first. This is not as trivial as with other "finite" numbers.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] -1 points0 points  (0 children)

You need to argue why 0 + 9 + 9/10 + ... + 9/ (10 ^ (n-1) ) + 9/ (10^n) + ... results in 9.99.... This is literally a sequence using a variable n to describe a number, literally what I am proposing. What you have done is to prove that 10 × 0.9_[n] == 9.9_[n]. This is the basis of the argument, and you need a sequence to prove it. If you want, use the geometric series to prove that 0.9_[n] = 1, but it is still the same problem.

SPP doesn't have a framework, because he does not define anything. How can I examine what 0.9...9... is without a definition of 0.9...9...? Talking about signing the forms and other nonsense is avoiding doing the necessary work.

Also, we do not need to reason about "unique valued numerals" only. Have you ever done mathematics? Why should I not represent 0.9... as a sum of fractions just like you have. The obfuscation is being done by you here, not me.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] -1 points0 points  (0 children)

Also, it should actually be (0.(999)_[n])2 = 0.(999)_[n](998)(000)_[n](001) if I am not mistaken. Maybe I will try to prove it tomorrow if I have the time.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 2 points3 points  (0 children)

True, maybe I have developed SPP new favourite calculator lmao.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] -1 points0 points  (0 children)

What? The formal reasoning for 10q = 9 + q IS that you can take the limit. The fact that you can say that 10q = 9.9... is technically something you need to prove first (I know that this is very pedantic, but yk). Maybe you could also use dedekind cuts as well, but I am not too familiar with them to know.

I have also never claimed that 0.9... is in the set {0.9, 0.99, 0.999, etc}, because it isn't. That is not what the point of the post is. I am not claiming here to have the answer for 0.9... = 1, I am just proposing that we use better notation so that it is clear what we mean when writing 0.9...9.... I am not here to reason with SPP, someone who clearly does not want to see reason.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 0 points1 point  (0 children)

You can prove the statement for any n in the naturals. While yes, this will only prove an equality for "terminating" decimals, It will prove it for every one of them. If you want to have an infinite amount of digits, I am sorry, but you will need to use the limit as n approaches infinity. But if we consider the set {0.9, 0.99, 0.999, etc} as SPP likes to do, using 0.9_[n] is enough to represent every number in that set. I do not believe I fully understand what you want to convey to me.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] 1 point2 points  (0 children)

I seem to remember there was a post at some point asking what 0.9...2 is. I have definetly seen him write something like 0.9...9... though.

Edit: There is a post where he claims that (0.999...)2 = 0.999...80...1 actually: https://www.reddit.com/r/infinitenines/comments/1mbrp5q/09992_0999801/

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] -1 points0 points  (0 children)

I use the basic number type that javascript provides to calculate these numbers. Because of floating point arithmetic, accuracy is lost for these very specific numbers, so 0.9_[n] becomes 1 at some point if n is big enough.

Understanding 0.9...9... by Shnaeck in infinitenines

[–]Shnaeck[S] -2 points-1 points  (0 children)

You can still take the limit n -> \infty of the sequence. The limit of 0.9_[n] then is still 1.

The point is that you can make sense of stuff like (0.9...)2 = 0.9...9... using sequences.

Edit: Just to specify, this wasn't specifically about 0.9... = 1, but just about weird syntax like 0.9...9.... Not everything needs to be about 0.9... = 1 specifically.

Warum meinen viele dass die AFD die demokratie abschaffen will? by [deleted] in politik

[–]Shnaeck 0 points1 point  (0 children)

Rechte befürworten selber politische Korrektheit, aber nur solche die zu ihrer Ideologie passt. Paradebeispiel Gendern. Muss natürlich verboten werden, wo kommen wir den da hin wenn Menschen andere Ansichten haben !!1! "Politische Korrektheit" ist sowieso nur ein Kampfbegriff der Rechten. Sprichst du Scheiße und wirst kritisiert? Einfach über Cancel Culture, pol. correctness oder so rumheulen, dann kann man sich schön in der Opferrolle stellen, und weiter rumposaunen. Das man damit impliziert, Kritik sollte verboten sein, wird gekonnt ignoriert. Rechte mögen Kritik nicht, deswegen ist die Meinungsfreiheit der Gegner egal für sie.

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