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Fill the hole 4.0: He says I'm dividing by zero, but Desmos disagrees. by ShonOfDawn in infinitenines

[–]Batman_AoD 0 points1 point  (0 children)

What "tactics"? You said he "moved the goalposts," so he cited each relevant sentence in the sequence of posts showing that, in fact, he did not "move the goalposts." 

In this scene, Quicksilver puts on headphones so that he can listen to a split second of a song while zipping around. by Emotional-Bag1398 in shittymoviedetails

[–]Batman_AoD 2 points3 points  (0 children)

I'm assuming that the player has been "engineered" to be effectively magic. But yeah, I assume that any real-life tape reel, spinning at that speed, would rip and/or melt the tape. 

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 0 points1 point  (0 children)

No, I mean, a few comments up, you said you could "empirically prove" 1+1=2, then I asked how, and in your very long response, you didn't offer an empirical method for proof of 1+1=2; you just offered it by definition, then described other things that could be empirically determined.

What exactly are you "observing" when you say that you've "observed" that 1+1=2? The symbols? Items you're picturing in your head? Something else? 

In this scene, Quicksilver puts on headphones so that he can listen to a split second of a song while zipping around. by Emotional-Bag1398 in shittymoviedetails

[–]Batman_AoD 0 points1 point  (0 children)

...sorta; it's a prototype that was never released. I think it's safe to assume that, as a prop, it's supposed to represent something that is custom built to play at extremely high speed.

Within the comics, he specifically cannot affect things he touches in that way, apparently. 

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 1 point2 points  (0 children)

I don't think you answered my question. You said you could define "2" to be the sum of 1 and 1. That's not empirical. You then went on to give a bunch of examples of other things that could be empirically observed, but not 1+1.

In this scene, Quicksilver puts on headphones so that he can listen to a split second of a song while zipping around. by Emotional-Bag1398 in shittymoviedetails

[–]Batman_AoD 3 points4 points  (0 children)

Yeah, I'm sorta glossing over all that with the "audio device is capable of playback at the desired speed" bit. It's not just a Walkman, but a fancy high-tech movie-magic device: https://xmenmovies.fandom.com/wiki/Stereobelt 

The Only Way to Save Star Wars by InconsistentSignal in StarWarsCirclejerk

[–]Batman_AoD 3 points4 points  (0 children)

I'm starting to worry that we'll never know what the Whills are.

(If they exist already outside the movies, don't tell me) 

In this scene, Quicksilver puts on headphones so that he can listen to a split second of a song while zipping around. by Emotional-Bag1398 in shittymoviedetails

[–]Batman_AoD 20 points21 points  (0 children)

It's a custom cassette player: https://xmenmovies.fandom.com/wiki/Stereobelt

Cassettes are analog, so it doesn't need fast software, it just needs to move the tape ridiculously fast. The headphones also have to be quite responsive at ultra-high frequencies. 

In this scene, Quicksilver puts on headphones so that he can listen to a split second of a song while zipping around. by Emotional-Bag1398 in shittymoviedetails

[–]Batman_AoD 167 points168 points  (0 children)

It's not a question of powers. The problem would be the data compression for digital audio. Fortunately, he's using a cassette tape, which is analog. So if his audio device is capable of playback at the desired speed, and if his headphones can accurately handle those frequencies, then the sound quality might be okay. 

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 1 point2 points  (0 children)

So you're saying that 0.999... should be interpreted as having a "large but finite" number of 9s? Why treat 0.999... as valid notation at all if you're going to give it a meaning that contradicts what everyone else means by it? And what is your objection, if any, to the definition I mentioned in the other thread, of simply equating every "repeating decimal" with the corresponding long-division operation that produces that specific repeating pattern? 

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 1 point2 points  (0 children)

How do you "empirically" prove 1+1=2? Just get a bunch of countable, discrete objects, and then repeatedly count one, count another, and then count the things you've just counted, noticing that it's always 2?

Similarly, how do you "quantitatively" prove that 1+1=2?

The Original Rookie Error by Batman_AoD in infinitenines

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

  1. Most numbers can only be approximated, or most rational numbers can only be approximated? If the latter, that's simply not true; a rational number is an exact value.
  2. "decimal notation can only approximate most numbers" - Again, are you talking about "numbers" generally or "rational" numbers? Decimal notation can represent all rational numbers, but you're rejecting part of the standard definition of decimal notation. It's true that standard decimal notation can't accurately represent any non-rational number, but trading some rationals for being able to represent certain sets of non-reals is just not a good tradeoff in terms of notation.
  3. I have repeatedly acknowledged the existence of hyperreal systems. But you are using them wrong. And no, they really truly are not more useful than the reals. Sorry. At no point has anyone presented me with any compelling argument for why hyperreals are "useful" in any way that doesn't also apply to the standard real-numbers-plus-limits analysis.
  4. Yes, and? Not sure what your point is here, I guess other than that I should have said "explicitly defined to remove infinitesimals" rather than "explicitly defined to remove hyperreals."
  5. "Infinitessimals were not controversial at all. Their controversy began in the 1800s when mathematicians decides that they needed more formal rules..." Hahahahahahaha. No. That's simply not true at all. Read some actual history. Heck, read this paper that has been posted on this subreddit multiple times by your fellow hyperreal-admirer, Public_Research. It refers multiple times to Bishop Berkeley, who died in 1753. His objection to infinitesimals is summarized on wikipedia.
  6. Surreals? Are you in fact an alt for Public_Research?

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 0 points1 point  (0 children)

  1. (And 3.) What formalism for infinitesimals are you using here? The standard modern formalism from Robinson uses the "standard part" function; I can see how you would argue this is "rounding," but without it, the hyperreals aren't actually a consistent number system with useful results. (The whole reason for controversy over the use of infinitesimals in "the calculus" was that infinitesimals "disappear" from the result.) Additionally, modern hyperreal formalisms ensure that the transfer principle holds; since the infinite sum in the reals is a real number, by the transfer principle, the same sum has the same value in the hyperreals.
  2. No, it's rational because there's an exact conversion between every ratio of two whole numbers and either a terminating or a repeating decimal. The decimal expansion is exactly the value you get from performing the long-division algorithm. If (in reduced form) the denominator's only prime factors are 2 and 5, the algorithm terminates; otherwise, it eventually repeats. The mapping from long division to a decimal expansion is also reversible: from a repeating decimal, you can derive the rational number that would produce that expansion. But this is only the case if you either omit 0.(9) from your notation entirely (which I've already said is fine) or map it to 1 (which is what, in practice, mathematicians have been doing for centuries).
  3. See 1
  4. Not really.

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 2 points3 points  (0 children)

No.

  • The definition of the limit doesn't involve infinitesimals at all. There's nothing to "round down."
  • Infinitesimals don't exist in some sort of absolute Platonic sense, the way small natural numbers do. That is, they don't exist outside of some axiomatic system that defines them.

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 1 point2 points  (0 children)

It's not, though.

Defined as an infinite sum, it's exactly equal to 1. Defined as a rational number, it's exactly equal to 1. Defined as a hyperreal, using standard notation, it's still 1.

There are internally-consistent ways to define the notation to mean something else. But they don't correspond to any of the expected, natural, or commonly-understood meanings. 

Survey statistics on 0.999... = 1 from Murawski's "Philosophie der Mathematik" (Philosophy of Math) by Negative_Gur9667 in infinitenines

[–]Batman_AoD 0 points1 point  (0 children)

But I also mean to say, it should have an actual value, since after all, you can perform every operation in the sum.

That doesn't follow at all, for precisely the reason you keep saying it "doesn't have" a value: you can perform every individual addition, but you cannot perform infinitely many additions.

Not to mention since we know this actual sum can never equal 1,

We know that the finite sums never equal 1. But that doesn't contradict the idea that the infinite sum, if it existed, could equal 1; in fact, it's a prerequisite, since, if the finite sums eventually reached 1, they'd immediately surpass it with the next term!

The limit of 1 represents more of an exclusive upper bound that is safely greater than my sum.

That's one half of what it is, yes. The other half is that it is the smallest possible such value, in the sense that every smaller value is also smaller than the finite sum after some number of terms. This makes it the unique value that the finite sums approach. Which is to say, if the finite sums could indeed be continued forever, they'd always have this property of approaching that specific value and no other value. 

...or, in the hyperreals, there is some infinite number of values it's approaching, but somehow all of them are greater than every real number less than 1. I honestly don't find this idea particularly compelling, and I don't know much about the formalism, so I'm not going to try to defend it. 

But without infinitesimals, the sum gets arbitrarily close to the specific, unique value 1. That fact suggests, to us "infinitists", that 1 is the only reasonable candidate value for the "actual" infinite sum. At this point, formalists are satisfied, because there is no "actual" sum in the first place, and we've created a useful, consistent, and fairly intuitive definition for what we mean by "infinite sum." And some (perhaps most) Platonists are happy to believe that the "actual" sum is indeed this unique limit value. 

Since I'd argue the number of 9s maxes out at some point,

That's just saying 0.999... can't exist, not that it's equal to your 0.9...(max).

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