Hah no worries. Thanks for being so reasonable yourself lmao.

Fair points. The latter case is basically where my concern is.

I think you are assuming a level of competence from people that I don’t have faith people actually have. People absolutely can and do take “you cannot prove a negative” as a real logical rule in the literal negation sense. This isn’t colloquialism. This is people misunderstanding what the phrase means.

I have definitely had conversations with idiots that have taken this phrase to mean that you just literally cannot logically prove negated statements. Whether folks like you get that that is not what the phrase refers to is irrelevant to why I’m pointing out the distinction.

If you subscribe to classical logic (i.e., propositonal or first order logic) this is not true. Proof by contradiction is one of the more common classical logic inference rules that lets you prove negated statements and more specifically can be used to prove nonexistence statements in the first order case. People go so far as to call the proof by contradiction rule “not-introduction” because it allows you to prove negated things.

Here’s a wiki page that also disagrees and talks more specifically about this “principle”: source (note the seven separate sources on various logicians/philosophers rejecting this “principle” as well).

If you’re talking about some other system of logic or some particular existential claim (e.g. existence of god or something else), then I’ve got not clue. But this is definitely not a rule of classical logic.

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

This feels pretty fucking dumb.

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.

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.

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.