By way of contraction, suppose there exists some collection of non-interesting numbers. According to the well-ordering principle of nonnegative integers, this set has a minimal element, x. However this makes x interesting: a contradiction. Therefore, all numbers are interesting. Q.E.D.
Doesn’t this mean that all non-negative numbers are interesting?
You could do the same with negative numbers, but the greatest element is interesting. And then zero is the only non negative and non positive number, so it’s interesting as well. The proof is incomplete, but easily finished.
My issue is less with the integers, but more with non-ordered fields. I think this implies that there are non-interesting complex numbers, for example.
Yes I was of course not being completely technical. The idea was to not make it overly complicated and use “number” to mean what most people typically think of when they talk about interesting numbers, their favorite number, number theory, etc: these being non-negative interegers or natural numbers.
However, you raise a good point when thinking about the extension of this to the integers, real numbers, complex numbers, etc. As @the-poetic-mathematician mentioned, it is easily extended to integers. But, we run into issues with the reals; there is no well-ordering of the reals and even worse, for complex numbers, there is no usual ordering at all (Complex numbers are not comparable in a less then, greater than way. At best, they can be partially ordered via complex modulus, i.e., absolute value.)
At the same time, just because we cannot use well-ordering doesn’t mean we can’t fix the proof for reals, complex, etc. So there still may be hope for all numbers.
Let F be a non-empty set, and let M be the subset of F containing all utterly uninteresting members of F.
Let {I_n} (n is a natural number going from 1 to infinity) be a countably infinite series of subsets of M, chosen so that these subsets can be ordered by some method into {I_n} so that I_n+1 >= I_n for all n. (Iff M is a finite set, then there exists some natural number N for all n>N, I_n=I_N, and iff M is the empty set, then for all natural numbers n, I_n is also the empty set)
Let us assume in contradiction that I_n isn’t empty, and that there ARE some utterly uninteresting members in F:
Because I_n is ordered, we must get that for any natural n, I_1 <= I_n; therefore the members I_1 are the FIRST utterly uninteresting members of F under the ordering method we have chosen, and that makes them at least SOMEWHAT interesting.
That runs IN CONTRADICTION to our definition of I_n, according to which there can’t be ANY interesting members in I_1, and therefore the assumption of I_n being non-empty must be false. ->
-> for all n, I_n must be the empty set ->
-> M is also the empty set ->
-> There are no utterly uninteresting members in F.
Q.E.D.
Hmmm. I think we may need to consider the case when l_1 = l_2 = … = l_n = … right?
Also we should be careful about claiming everything is interesting; not everything can be put into a set, e.g., the collection of all groups is not a set 😦 So your proof would not apply to all groups, just F := any set of groups.
on the subject of bots, runescape had literally the best way of dealing with their botting problem:
if an account was detected using bot software, they would be instantly teleported to a hearing from a witchfinder general style npc, where other players could watch and throw rotten tomatoes at them. then the audience could vote on how the person on trial would be killed as punishment, and THEN the botter was permanently banned afterwards. it was the funniest shit ever
tbt when they had no banning system so the gms just teleported hackers into The Void™ for eternal punishment
That was a whole other problem in itself, due to the whole “disc of returning” debacle.
Basically there was an item (disc of returning) that let regular players visit these “banned” players in the void. You could come and go freely and still talk to any banned people there. The only problem was that this item was totally tradeable/droppable, and people visiting were getting tricked by the banned players into giving the item up to them, or dropping it so it would despawn.
Basically people were pulling some body-snatcher shit, and banned players were taking the place of innocent players through the disc of returning to get back into the game, and leaving behind the innocent ones trapped in their place. Runescape was fucked up lmao
them: whats signs do you have that capitalism is killing people? what signs do you have that it’s worsening their lives?
me:
article don’t even mention the drastic increase in liver problems among young people 😦
Three Buck Chuck is cheaper than psych meds and therapy
¯_(ツ)_/¯
capitalism has turned people into commodities, we no longer see ourselves as human beings but things that must produce worth. we start feeling like we’re losing our production value and we end it.
“this is why we need a platform with 0 censorship!” no its not actually, because this platform was ridden with fucking child porn
this entire mess is because tumblr didnt have any fucking moderation, and they let it get worse and worse until eventually they had to resort to dumbass overreaching solutions that dont solve anything. the solution isnt “judgement free uwu” social media. the solution is actually moderating your site to keep that shit off of it
tumblr sucked yet its the only thing people like us could ever have posted on. tumblr was a deep sea geothermal vent and we are all pallid, desperate crabs snapping at the dark toxcic nutrients spweing from its hole, and bringing us into the harsh light of the instagram influencersphere would kill us instantly.
Iron in the Sand 