I can't email you, since you've removed your email address from your profile?
Seriously, Zachary, go right back to the nomination page and the questionnaire and undelete your announcement and answers. Just wait on any decisions, please; I'm begging you. We need someone exactly you to join the mod team;
I actually think that it is an interesting sort-of philosophical question, but I am not sure that I am convinced that it is really a question about math. Any input from the gallery?
This is not an answer. The question asks for intuition about why function $x \mapsto \mathrm{e}^{\frac{1}{2}x}$ is a good guess, not for a proof that it works.
That the answer was accepted is, frankly, shocking to me.
That being said, the question itself isn't all that good, and I would like to humbly suggest that it be deleted.
@ZacharySelk Please don't. The site is (still) so toxic because we have too few people like you. It is not too late to save the site, but we have to all work together and not let the toxic spewers eliminate us one by one.
@XanderHenderson It's just a trivial special case of the general combinatorial fact called PIE (principle of inclusion and exclusion).
Now who doesn't like PIE?
@XanderHenderson I deleted the question, firstly for the reason that it should have been a clarification comment on the original answer, and secondly for the reason you gave.
@user21820 I agree that inclusion-exclusion plays a role, but I don't think that the question is about inclusion-exclusion. The question seems to be about why $\lnot A$ is often "easier" to deal with than $A$; the answer is (I think) essentially inclusion-exclusion and de Morgan, but I don't think that is what the question is asking.
In any event, it is closed now, and I can't say that I feel all that strongly about it, so a result has been achieved.
@XanderHenderson In the case of this particular question, which is about counting, I think PIE is the main reason why some combinatorics problems are hard to do directly but easy to do once you switch to the complement. Simply put, PIE is the most common combinatorial identity that is actually non-trivial. In general, one is just asking why different perspective sometimes produces a simpler proof, which is just a truism.
@XanderHenderson: I'm not saying it's what the question is asking, but I'm saying that PIE is the most satisfying answer I want to get at the point where I had a similar kind of question and didn't yet have the answer I gave.
@ZacharySelk If you want to withdraw from moderator election then that's absolutely your choice because handling toxicity like the one you faced is probably a routine job for moderators. But regarding deleting your profile, please think again.
That's a really refreshing idea, @XanderHenderson or DEBRUC. But "BRUCED" sounds more natural. And it gets rid of the incorrect perception that CRUDE is crude.
