myslsl

myslsl , 2 hours ago to Science Memes in I just cited myself.

Yes, informally in the sense that the error between the two numbers is "arbitrarily small". Sometimes in introductory real analysis courses you see an exercise like: "prove if x, y are real numbers such that x=y, then for any real epsilon > 0 we have |x - y| < epsilon." Which is a more rigorous way to say roughly the same thing. Going back to informality, if you give any required degree of accuracy (epsilon), then the error between x and y (which are the same number), is less than your required degree of accuracy

myslsl , 2 hours ago to Science Memes in I just cited myself.

You are just wrong.

The rigorous explanation for why 0.999...=1 is that 0.999... represents a geometric series of the form 9/10+9/10^2+... by definition, i.e. this is what that notation literally means. The sum of this series follows by taking the limit of the corresponding partial sums of this series (see here) which happens to evaluate to 1 in the particular case of 0.999... this step is by definition of a convergent infinite series.

myslsl , 3 hours ago to Science Memes in I just cited myself.

He is right. 1 approximates 1 to any accuracy you like.

myslsl , 1 day ago to Technology in Music industry giants allege mass copyright violation by AI firms

Given that music boxes are very very old it is plausible that beethoven could have made a remark sharing his opinion on this exact issue. I don't mean to agree/disagree with your point, I just find that kind of interesting.

myslsl , 1 day ago to Technology in Music industry giants allege mass copyright violation by AI firms

You're getting downvoted but you are right. Stuff like this is a super cool example of exactly the type of thing you are talking about imo.

There's a lot of AI generated art that sucks. But that does not imply that in skilled hands an artist can't use those tools in creative/interesting ways.

myslsl , 1 day ago to Technology in Music industry giants allege mass copyright violation by AI firms

Arguably a lot of these tools are designed specifically to reduce the effort a human has to put in to create the art they want to make too.

myslsl , 1 month ago to Math Memes in wholesomeness

Not sure what "numerical oscillations in 2d" means? The picture is a 3d graph?

myslsl , 3 months ago to A place for everything about math in [Solved] Algebraic Solutions to Graphical Trig Problems?

It does if you claim to know cos (A) = 1.

My issues with this are: Your solution did not originally claim this, it is not stated anywhere in the problem and it leads to exactly the same kind of foundational issues in the context of showing "algebraically" why cos(x)=1 at integer multiples of 2pi now.

The question as given is illposed. You have to know something. If not, why not ask a philispohical question like what is trigonometry even?

Agreed. It's at least vague/misleading. This is apparently for a precalc clep exam, so the only real sane definition a student would know to fall back on here would be geometric definitions for sine and cosine. What I think the intent of the problem is, is to build intuition on knee jerk facts about sine/cosine rather than something particularly formal?

myslsl , 3 months ago (edited 3 months ago) to A place for everything about math in [Solved] Algebraic Solutions to Graphical Trig Problems?

Rewriting the problem as solving sin(A)=0 and then claiming outright that A must be an integer multiple of pi doesn't really help as far as I can tell, since that is just the original problem with x exchanged for A?

myslsl , 3 months ago to A place for everything about math in [Solved] Algebraic Solutions to Graphical Trig Problems?

I realized in retrospect I misread the header so I apologize for that.

I'm still betting they aren't expecting a true algebraic or analytic solution here. Things like finding max/min points, finding arbitrary particular values of trig functions, solving trigonometric equations and so on can be notoriously hard in the absence of geometric reasoning/intuitions.

Later on if you decide to study calculus you might eventually see the sine and cosine functions defined rigorously via infinite series. That may sound convoluted, but part of the purpose of doing that is because of the difficulties of the issues mentioned above. Basic sounding facts like: What is sin(0.1234)? are not so easy to answer where you are at but can be dealt with more conveniently using these kinds of tools from calculus.

The questions being asked here are also just kind of typical knee jerk facts that most people want students coming out of a trig class to just know.

I think your reasoning geometrically seems very on the right track. Appealing to the unit circle or the graph of y=sinx for these feels correct in the sense of what a trig student would be expected to know coming out of or during a trig course.

myslsl , 3 months ago to A place for everything about math in [Solved] Algebraic Solutions to Graphical Trig Problems?

Okay, I see. I'm fucking blind and did not see the words "algebraic" literally at the top of the screenshot.

For what it is worth, they could just be referring to how they are representing the problems they are asking rather than the form of the intended solutions with that.

myslsl , 3 months ago to A place for everything about math in [Solved] Algebraic Solutions to Graphical Trig Problems?

The point they made was correct. Arcsine by itself only gives one of the two solutions to sinx=0. It seems like they already realize that they need to use arcsine carefully if they use it at all.

myslsl , 3 months ago (edited 3 months ago) to A place for everything about math in [Solved] Algebraic Solutions to Graphical Trig Problems?

There's nothing here that tells you that you need to use some technique from algebra explicitly as far as I can see?

Edit: I misread. See my follow up comment too.

The usual trig functions like sine and cosine are famous examples of transcendental functions so I very seriously doubt there is some clever algebra trick you're missing that the author intends you to do.

I'd assume your instructor (or the author) is expecting you to use your geometric knowledge about the unit circle on these if you haven't covered inverse trig functions yet. But I also can't really read their mind, so your best bet might be to just directly ask them?

Edit: This could also depend on what trigonometric identities you know so far too.

myslsl , 3 months ago (edited 3 months ago) to Science Memes in hmmmm

My dear friend, I am very big fan of the back-pedaling you're doing here. I want to also point a couple things out to you.

I’ve never argued that mathematics has a concept of finite or infinite numbers, or not. All that I have argued is that what the math world identifies as infinite, is not actually infinite when applied to the real world.

This is blatantly untrue. You can certainly play the post-hoc "oh but I meant..." game and slowly change your argument to be something different, but what you said originally is not what you are suddenly now claiming here and your lack of logical precision or clarity in the claims you make is certainly not my fault or my problem. Consider taking a course in mathematics to firm up your logical argumentation skills?

Let me remind you of a couple other claims you have made beyond what you are suddenly now pretending you claimed:

1. "Infinity cannot be divided, if it can then it becomes multiple finite objects."
2. "If infinity has a size, then it is a finite object."
3. "There is no infinityA or infinityB there is just infinity itself."
4. "The statement 'some infinities are bigger than other infinities' is an illogical statement".
5. "The mere statement that there are multiple infinities, negates either objects identification as being infinite, and reduces both objects to finite objects (more word salad follows)..."

Of course you have made a bunch of other claims in your weird psycho-babble word salad too. These are just some highlights.

Lets consider this thing you just said here though: "what the math world identifies as infinite, is not actually infinite when applied to the real world". You know, this sounds very familiar. It is almost like my very first comment to you was "It really depends on what you mean by infinity and division here." Real wild stuff huh? Almost like it is important to be clear on the definitions and senses of the words we are using right? Like we should be clear on what exact definitions we mean yeah? Hmm... This sounds so familiar.

As much as I'd love to make fun of you more while you rediscover arguments for/against mathematical platonism I'd rather move on.

As an engineer I deal with recursive functions, code that can run indefinitely. But as an engineer I understand that the code that is running needs an initiation point, the point at which the code is initially executed, and I understand that the seemingly infinite nature of the code, is bound to the lifespan of the process that execute it, for example, until the process is abruptly stopped, or power is taken away from the computer the process is running on. A lifespan invalidates the seemingly infinite nature of the code, from a practical sense. When you start to understand this, and then expand your focus to larger objects like the universe itself, you start to understand the finite nature of the material world we live in.

Loving the assumption here that I have no background in CS or software engineering.

I understand that mathematicians deal with abstraction. I deal with them too as an engineer. The difference is that as an engineer I have to implement those abstractions within the real world. When you do this enough times you will start to understand the stark differences between the limited hypothetical worlds math is reasoned about, and the very dynamic world the real world, that those math solutions are applied to. The rules of hypothetical worlds are severely limited in comparison to the real world. This is why it’s very important for me to define the real world boundaries that these math problems wil be applied to.

I don't think claiming practical experience as an engineer as justification for misunderstanding and drawing faulty conclusions from basic mathematics is really the gotcha you think it is here. On the contrary, if you really do have a background in engineering, then you should know better and it is now my opinion that the people who have taught you mathematics and the basics of engineering have done you a serious disservice for not teaching you better. Misunderstanding mathematical models is textbook bad engineering. What you are doing here is using your engineering background to justify why it is okay for you to be a shitty engineer.

I’m used to working with folks, like yourself, that have a clearly hard time transitioning from a hypothetical world to the real world.

Who is having the trouble? I'm not the one stumbling over basic things that children learn in high school algebra like what the definition of a function is.

This is why I have respond with civility, and have looked past your responses insulting tone.

Oh yes, clearly my tone is insulting, but yours has never once been insulting. You pure beautiful angel you. If only the rest of us could be such a pure and sweet soul like you. I'll be sure to only speak to you in the kindest and sweetest ways so that I don't hurt your very precious and delicate feelings in the future.

I understand it’s a fear response of the ego, and I don’t judge you for it. I understand that it’s difficult to fight with the protection mechanisms of the ego.

I'm sorry kind and gentle prince, but I can't help but point out that the projection here from you is very entertaining. I'm so very sorry for any hurt this may cause your poor delicate feelings.

myslsl , 3 months ago to Science Memes in hmmmm

I understand that you feel learning new things is hard. I sympathize with you. Lets start with a real easy one. High school algebra students often learn what mathematical functions are. You can handle that right? Tell me the mathematical definition of a function. Oh! Oops, I have accidentally linked you to a place where you can find the definition I'm asking you for in the first paragraph. Well, no going back now. Feel free to copy and paste the first paragraph of that link here.

Hmm, I wonder if there is a link between functions and finite/infinite sets? Oh gosh golly, perhaps they are related in some way? Almost like the definition of one requires some notion of the other?