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.

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.

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

On the bright side, you are now the proud owner of a hip designer bean plate.

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.

None of this includes the correct answers to the questions I asked you. I’m not going to read anything else from you until you correctly answer the questions I asked.

My degree is in math. I feel pretty confident in saying that you are tossing around a whole bunch of words without actually knowing what they mean in a mathematical context.

If you disagree, try the following:

1. What is a function? What is an injective function? What is a surjective function? What is a bijection?

2. In mathematics, what does it mean for a set to be finite?

3. In mathematics, what does it mean for a set to be infinite?

I’m willing to continue this conversation if you can explain to me in reasonably rigorous terms what those words mean. I’ll help you do it too. The link I sent you in my previous post that mentions cardinal numbers links you to a wikipedia page that links to articles explaining what finite and infinite sets are in the first paragraph.

To be clear here, your answer for 2 specifically should rely on your answer from 1 as the mathematical definition of a finite set is in terms of functions and bijections.

Here are some bonus questions for you to try also:

4. In mathematics, what does it mean for a set to be countable?

5. In mathematics, what does it mean for a set to be uncountable?

Infinity cannot be divided, if it can then it becomes multiple finite objects.

It really depends on what you mean by infinity and division here. The ordinals admit some weaker forms of the division algorithm within ordinal arithmetic (in particular note the part about left division in the link). In fact, even the cardinals have a form of trivial division.

Additionally, infinite sets can often be divided into set theoretic unions of infinite sets fairly easily. For example, the integers (an infinite set) is the union of the set of all integers less than 0 with the set of all integers greater than or equal to 0 (both of these sets are of course infinite). Even in the reals you can divide an arbitrary interval (which is an infinite set in the cardinality sense) into two infinite sets. For example [0,1]=[0,1/2]U[1/2,1].

Therefore there cannot be multiple Infinities.

In the cardinality sense this is objectively untrue by Cantor’s theorem or by considering Cantor’s diagonal argument.

Edit: Realized the other commenter pointed out the diagonal argument to you very nicely also. Sorry for retreading the same stuff here.

Within other areas of math we occasionally deal positive and negative infinities that are distinct in certain extensions of the real numbers also.

If infinity has a size, then it is a finite object.

Again, this is not really true with cardinals as cardinals are in some sense a way to assign sizes to sets.

If you mean in terms of senses of distances between points, in the previous link involving the extended reals, there is a section pointing out that the extended reals are metrizable, informally this means we can define a function (called a metric) that measures distances between points in the extended reals that works roughly as we’d expect (such a function is necessarily well defined if either one or both points are positive or negative infinity).

“The cardinality of the integers is equal to the cardinality of the real numbers, which is called the continuum hypothesis.”

The cardinality of the integers is not equal to the cardinality of the reals. The integers are countable (have the same cardinality as the natural numbers). A very famous proof in set theory called Cantor’s diagonal argument shows the reals are uncountable (i.e. not countable).

The continuum hypothesis is also not about comparing the cardinality of the reals and the integers or naturals (since we already know the above). The continuum hypothesis is about comparing the cardinality of the reals with aleph_1.

Within the usual set theory of math (ZFC set theory), we can prove that we can assign every set a “cardinal number” that we call its cardinality. For finite sets we just assign natural numbers. For infinite sets we assign new numbers called alephs. We assign the natural numbers a cardinal that we call aleph_0.

These cardinal numbers come with an ordering relationship where one set has a cardinality larger than another set if and only if its associated cardinal number is larger than the other sets cardinal number. So, alepha_0 is larger than any finite cardinal, for example. There is a theorem called Cantor’s theorem that tells us we can continually produce larger and larger infinite cardinals in fact.

So, we know the reals have some cardinality, thus some associated cardinal number. We typically call this number the cardinality of the continuum. The typical symbol for this cardinality is a stylized (fraktur) c. Since aleph_0 is countable, every aleph after aleph_0 is uncountable. By definition aleph_1 is the smallest uncountable cardinal number. The continuum hypothesis just asks if aleph_1 and c are equal.

As an aside, it is provable that c has the same cardinality as the powerset of the naturals. We let the cardinality of the powerset of a set with cardinality x be written as 2^x. Then we can write the continuum hypothesis in terms of 2^{aleph_0} and aleph_1. The generalized continuum hypothesis just swaps out 0 and 1 for an arbitrary ordinal number alpha and its successor in this new notation.

This issue is not a black and white speak english vs not kind of thing. There’s no shortage of immigrants that speak english perfectly well sans a minor accent but are discriminated against and treated poorly anyway for not being native speakers.

Edit for those who downvoted: I am a native english speaker. I have been discriminated against based on my regional accent. Only a fucking fool would think the same things don’t happen to nonnative speakers.

Part of the goal here isn’t even mastery of the language itself. Exposure to new cultures is important. Being able to empathize with how hard learning a language is is also important.