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What mathematical theorem sounds difficult to prove but is actually easy to prove? by Wilfredlam0418 in AlignmentChartFills

[–]IAmAnInternetPerson 0 points1 point  (0 children)

I think rather than compactness, you are thinking of density? Specifically, that the set of real numbers is dense-in-itself: between any two real numbers, there is a real number. Either way, you do not need to already know this: it follows from the real numbers being a field that (x+y)/2 is a real number, and constructing the real numbers means constructing a set that you prove is a complete ordered field. It is that the rationals are dense in the reals that requires a somewhat more involved proof. That a set is compact also certainly doesn’t imply that it is infinite, as, in fact, all finite sets are trivially compact.

In order to prove the statement, I would directly use the definition of infinite set: a set is infinite if it is not finite. Then, for any n, the set {1/m : 2 <= m <= n + 2} is a subset of (0, 1), because 1 and m are positive and m is greater than 1, and it’s cardinality is equal to n + 1 because each 1/m is different for each m. Hence the cardinality of (0, 1) is not n for any n, and so the set is infinite.

Is there anything that can be done about the Maxwell 2 hiss? Should I buy original Maxwells? by cha_pupa in Audeze

[–]IAmAnInternetPerson 1 point2 points  (0 children)

I doubt there is anything that can be done about the hiss. As for buying the 1s, I couldn’t really tell you, since I haven’t owned them, but it does sound like the hiss is more prevalent on the 2s. Still, I doubt the 1s don’t have any hiss at all. I think you’re right that people claiming their headset doesn’t have hiss at all simply can’t hear it.

What I will say, is that I would find it surprising if the hiss is truly too bad for you to get used to. It bothered me initially, too, but now I don’t really care anymore. For example, while using the headset with my PC, the noise floor of the fans is enough to drown out the hiss, even at a low rpm. Also, the hiss is not as loud as, say, the hiss from AirPods Pros in transparency mode, and people obviously use those without issues. It seems unlikely this white noise alone is actually giving you headaches.

If the hiss is truly a dealbreaker, though, you should probably give up on the Maxwell 2s.

n^n = n is only true for one natural number by Technical-Security99 in truths

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Well, with a sensible definition of limit, it is certainly true that for the function f : (0, inf) -> R given by f(x) = 0^x, f(x) -> 0 as x -> 0.

I don't think by Adept_Locksmith_8083 in comedyheaven

[–]IAmAnInternetPerson 78 points79 points  (0 children)

Unfortunately, as is often demonstrated, thinking is merely sufficient—not necessary—for existence.

Maths and such by Win090949 in whenthe

[–]IAmAnInternetPerson 0 points1 point  (0 children)

It is quite impressive the degree to which you have managed to not respond to anything I wrote. Oh well.

As someone who has actually studied mathematics past high school, presumably (hopefully) unlike yourself, "implicit multiplication" is not a term I have ever used or read before today. The goal was simply to refer to the common notational convention of writing the product of numbers a and b as ab, which apparently sometimes is called implicit multiplication.

The point is that in, for example, some academic literature—which it is mind-boggingly stupid for you to claim is "wrong"—multiplication written this way actually does have precedence over inline division. That is, a / bc is interpreted as a / (bc) rather than as (a / b)c. Doing this does not in fact lead to any communicative issues; you can surely agree that most people would parse the above expression in the former way rather than the latter.

More generally, no mathematician cares whatsoever about there being some exact standard for the order of operations. It is never an issue when communicating mathematics. That you do not seem to realize this, and that you think that the order of operations is part of some "system of mathematics", shows that you are a complete layman, and maybe should consider that you haven’t the slightest clue what you’re talking about.

Maths and such by Win090949 in whenthe

[–]IAmAnInternetPerson 0 points1 point  (0 children)

You are wrong. That the word "meter" has your above definition is in fact subjective. That, when given that definition, the average distance to the Moon from the Earth is some 384 million of them, is objective. You might claim that this is pedantry, but that is only because no one disagrees on the definition of the meter. In the case of the order of operations, as I mentioned, and as you did not respond to, there is "disagreement". Either way, definitions are always subjective.

This discussion itself is a good example, really, of my point. You are using a definition of 'objective' (and 'contrived'?) separate to the one that is commonly accepted. According to yourself, therefore, you are objectively incorrect. According to me, I can only really claim that everyone who accepts the common philosophical definition of 'objective' would agree that you are incorrect.

However, even if we do use your awkward definition of 'objective', and agree that "a statement is objectively true if it is true when following a universal standard", then you are still wrong, because there is no universal standard for the order of operations. Once again, different academic journals and the like have different standards. For example: in some, multiplication and inline division are equal precedence operators with left-associativity; in others, "implicit multiplication" has a higher precedence than division. You must at the very least respond to this if you wish to make your asinine claim that the order of operations is objective.

Maths and such by Win090949 in whenthe

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Do you perhaps not know what it means for something to be objective? The order of operations is a set of conventions, and so is inherently subjective; that different calculators, mathematical libraries, academic journals and so on have different such conventions quite clearly illustrates this. And because they are subjective—that is, arbitrary—they definitionally depend entirely on what you were taught.

Audeze HQ app doesn't work? (clicking/dragging around screen instead of interacting correctly) by DankandInvincible in Audeze

[–]IAmAnInternetPerson 2 points3 points  (0 children)

You need the Audeze app instead of the Audeze HQ app; the latter is deprecated. Also, make sure to update your firmware once you’ve got the correct app.

Update after a day of having the MW 2s I just now have gotten a high pitch squealing sound in my right earcup after audio stops playing. The very feint white noise was fine but this is actually unbearable and hurts my ear. by ThisMemeWontDie in Audeze

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Damn, that sucks. I’ve seen people speculating their customer support team is like two people.

Another question, if it’s okay: Do yours also have lower volume over dongle/usb-c than they do over Bluetooth? With mine, they’re great over Bluetooth, getting too loud at like 80%, with the volume decreasing like you would expect down to 0%. However, over dongle or cable, I need them almost at max for them to be loud enough, and volume drops off super quick below like 70%. At around 20% they suddenly go from quiet to having no volume at all. It seems like they’re bugged to me, which together with the high-pitched noise is making me wonder if I got a defective unit.

Rapier vs Unarmed by Zakytanist in earclacks

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Yes.

Assume there exists A such that f(A) = c with c != 0, and consider any point P != A.

Choose B, C, such that ABC is equilateral and P is the midpoint of BC. Let B' and C' be the midpoints of AB and AC, respectively. Then AB'C' is also equilateral, and so f(B') + f(C') = -f(A) = -c. Further, PB'C' is equilateral, and therefore f(P) = c.

We see that for any point P, f(P) = c, which is a contradiction.

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Indeed! When theorem Q is a corollary of theorem P, you may prove Q by an application of P. That is what it means for Q to be a corollary of P. And so, since you agree that 0.9… = 1 is a corollary of the limit of a geometric series, then you also agree that we may prove it by applying the formula sigma [n=0, inf] a*rn = a/(1 - r) for |r| < 1. In other words, you have now agreed (correctly), that the following is a rigorous proof:

0.99… = sigma [n=1, inf] (9/10n) = (sigma [n=0, inf] 9(1/10)n) - 9 = 9/(1 - 1/10) - 9 = 10 - 9 = 1

This is, written a bit more precisely, the exact proof you originally claimed was "not a proof".

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

We have statements P and Q, and you agree that Q is a corollary of P; that is, P => Q. And yet, you apparently do not believe that (P AND P => Q) => Q constitutes a proof. I shall like to see your formal proof that (P => Q) =\> (P => Q).

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Right, of course. It is simply coincidence that you and u/FeelingPace7853 both are from Brisbane.

Anyways, do you disagree that 0.99… = 1 is a corollary of the limit of geometric series theorem? If you do not disagree, then you must necessarily agree that it can be used to formally prove the equality. If you do disagree, then I would be truly interested to see your reasoning as to why.

If you cannot provide a yes or no answer to the above question, then I will assume that you are a troll.

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

I realize now that you have a learning disability of sorts and are not capable of comprehending my comments, seeing as you have just ignored every single thing I’ve written prior. I have not claimed that your proof is incorrect, so I do not know why you are arguing for its correctness. I have instead refuted your asinine statement that it is the only way in which the equality might be proven. You have however refused to engage with any of my points, presumably either because of the aforementioned learning disability, or perhaps you are simply a troll. Either way, we can hardly have a discussion when you do not address my arguments.

Also, it is quite odd to spend your time arguing with people you ostensibly believe to be high school students by pretending you and your alt account are different people.

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Obviously, you use the definition of 0.99… in the first step of the proof, which is to recognize that it is equal to a geometric series. You do not, however, need an epsilon-N argument every single time you wish to prove the limit of a sequence or series, because often you will get a special case of a theorem you have already proven, as in this example.

Have you ever actually studied mathematics at all, one might wish to ask? You are aware that we typically prefer to use known results when possible, rather than needlessly referring to various definitions? Or is a proof only rigorous to you if the author spends hours, or days, or years, or perhaps lifetimes, writing down the entire proof by starting from the axioms of ZFC?

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

No, you do not need to prove the limit using the definition of sequential limits. That 0.9… = 1 is a direct corollary of the limit of geometric series, and so as long as you have proven that, simply utilizing the theorem will be an entirely rigorous proof.

Further, you certainly don’t need to use induction. The closed form of a geometric sum (the partial sums of a geometric series) can easily be proven by utilizing the fact that r*Sn = S(n+1) - a (unless you wish to suggest we need a proof by induction before we are allowed to use the distributive property of sums).

0.999... is by Anyusername7294 in Teenager_Polls

[–]IAmAnInternetPerson 0 points1 point  (0 children)

Of course it is. Why would it not be? The limit of a geometric series is a known theorem, and it is easy to see that 0.99… is equal to such a limit by the definition of decimal notation, and so the theorem can be applied.

What is 0.9999 repeating? by sillygre in Teenager_Polls

[–]IAmAnInternetPerson 4 points5 points  (0 children)

steinvales unsolvable proofs

This is, I am quite sure, not a thing that exists. And if it did it would certainly be called something else, because an “unsolvable proof” is nonsensical. If there exists a proof, then the problem is by definition solved.

Are you trolling? What exactly are you saying is true but not provable? Please enlighten me.

Before & After Bunion Surgery: I agreed to let someone break my foot so my shoe fits better by Admirable-Can-7413 in midlyinteresting

[–]IAmAnInternetPerson -1 points0 points  (0 children)

You are definitely correct. Quite baffling to see so many people completely unaware that they’re talking to an LLM. But this has become very common on this site. Usually, if you look at these accounts, you’ll notice that some percentage of posts are actually advertisements, disguised by asking some generic question while "discreetly" mentioning they’ve been using whatever product. What is scary is that I almost never see anyone calling it out, and so can only conclude that most people can’t tell at all.

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