I’m sorry my mom called you “pretty fucking dumb”. I know that must have hurt your feelings.

This feels pretty fucking dumb.

Ain’t nothin’ but a heartache.

The punchline here is a little compact. I don’t feel like it really gives the closure I need. Maybe if the basis for the joke had more continuity the humor would be less discrete.

I will fucking piledrive you if you mention AI again.

Some software can be pretty resilient. I ended up watching this video here recently about running doom using different values for the constant pi that was pretty nifty.

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

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.

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

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.

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.

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.

Eigenvectors, values, spaces etc are all pretty simple as basic definitions. They just turn out to be essential for the proofs of a lot of nice results in my opinion. Stuff like matrix diagonalization, gram schmidt orthogonalization, polar decomposition, singular value decomposition, pseudoinverses, the spectral theorem, jordan canonical form, rational canonical form, sylvesters law of inertia, a bunch of nice facts about orthogonal and normal operators, some nifty eigenvalue based formulas for the determinant and trace etc.

My experience with eigenstuff has been kind of a slow burn. At first it feels like “that’s it?”, then you do a bunch of tedious calculations that just kind of suck to do… But as you keep going they keep popping up in ways that lead to some really nice results in my opinion.

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.

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?

I considered reading and responding to this big long word salad you sent me, but I realized you were just further demonstrating the three points from my last post. Lmao, good luck.

Edit: Feel free to show me you learned the definitions I asked you about by answering my list of definition questions I posed to you a while ago by the way. I’m still fine with continuing if you do that.

Oh okay.

If there are infinite numbers, then there’s 3 in there somewhere.

No, this is not true. Just because you have infinitely many numbers in some collection, doesn’t mean one of the numbers in your collection has to be 3.

Look at the number line. There are infinitely many numbers on the number line between 1 and 2. For example 1+1/2, 1+1/4, 1+1/8, … are in there (among many others). But all of the numbers between 1 and 2 are strictly smaller than 3, so none of them can be 3.

Alternatively, there are infinitely many numbers strictly smaller than 3, none of which are 3 either.

If 3 is not there then it’s not infinite.

Well consider the set of numbers 3+1, 3+2, 3+3, 3+4, … (the set of integer numbers strictly larger than 3). This set of numbers is also infinite and does not contain 3. So a set being infinite doesn’t imply it must contain the number 3.

Which statement?

To me you have demonstrated:

1. You don’t know even the most basic definitions of the things you are trying to talk about.

2. You are possibly too willfully stupid to bother to learn said definitions.

3. You are capable of babbling incoherently about things you do not understand ad nauseum.