Even in the best case scenarios you still have “I was a modern nazi” as a documented thing you did that you could end up needing to explain for the rest of your life. How plausible does “Oh, but I was secretly one of the good guys!” sound to you?

Ross+Nicolas=Rossolas

Even if the argument doesn’t persuade them at the time it still makes sense to point it out to them so that they are (hopefully) aware of it later.

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

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

I don’t have a don’t in this don’t.

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.

Wow. How fucking dare you? I trusted you.

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?

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.

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.

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

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?

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?

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.

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.