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

This feels pretty fucking dumb.

So you’re saying that because a religion allows you to choose which of God’s commandments, carefully passed down through every generation, you personally want to follow based on your gut feeling, can’t be shamed?

No, that is not what I said.

Why should the ones who choose to deny parts of their religion be seen as representative of it over those who’ve chosen to uphold them?

I definitely answered this in my original comment.

Because if the majority of people following a particular religion reject a prior view as false or wrong, then arguably that view is no longer part of the religion.

Religions aren’t crisp, unchanging, monolithic entities where everybody believes the same thing forever. If we’re talking about judaism in the sense of the views and practices jewish people actually subscribe to, then that seems like we are referring to beliefs they actually hold in a mainstream/current sense, not beliefs they previous held but now reject?

This seems a little hyperbolic of you.

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.

Operating System Concepts by Silberschatz, Galvin and Gagne is a classic OS textbook. Andrew Tanenbaum has some OS books too. I really liked his OS Design and Implementation book but I’m pretty sure that one is super outdated by now. I have not read his newer one but it is called Modern Operating Systems iirc.

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.

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.