1,524 karma · joined January 11, 2012
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You can 'represent' the process of summing an infinite number of positive powers of x as a formula. That formula corresponds 1:1 to the process only for -1 < x < 1. However, when you plug 2 into that formula you essentially jump past the discontinuity at x = 1 and land on a finite value of -1. This 'makes sense' and is useful in certain applications.
1) All of the heavy lifting is done sneakily by the word "purchasing." Of course "purchasing" something feels like you ought to own it, but did you "purchase" X or did you just pay for limited access to it? That's the entire debate, but this quote baits you into thinking of everything in terms of purchasing / panders to people that already do.
2) This quote amounts to "if paying cannot get you full ownership of X then getting a full copy of X for free is not stealing (so go ahead)." How about you always pay the creator and then pirate only for the additional ownership rights? I'm sure the quote reads that way to some people, but clearly it was crafted to also appeal to the "I just want stuff for free" crowd.
https://bbchallenge.org/1RB2RA1LC_2LC1RB2RB_---2LA1LA
For example: If in state B and the tape at the current marker reads 0: write 2, move the head Left once, and go to state C.
There is no known reason why we can't tell if any specific program halts. We just can't write code to tell if an arbitrary program halts. This result is exactly what you are using when talking about preferring BB(k) for some fixed k, each k requires solving a bunch of halting problems. The paradox proofs you seem to dislike are only needed for the general case, the general halting problem or, and this is to me the confusing part, the general BB(n). So you are comparing BB(k) for some fixed k to something infinitely more general in the general halting problem. So, again, why would you compare these two things? When is that a useful thing to do?
Can you clarify what you mean by this? You prefer one to the other in what circumstances?
> Now, the busy beaver numbers are enormous and we will likely never solve even BB(6). But that’s not for reasons of logical paradoxes like “this sentence is false” or “the smallest positive integer not definable in under sixty letters”.
Also please clarify this. BB is hard to compute because it is essentially defined in terms of solving the halting problem (that's known to be pretty hard). You alluded to a proof of that fact. What is your point? And what is your problem with those kinds of proofs? What do BBs have to do with undecidability besides being directly defined in terms of an undecidable operation?
The only argument is "well, then they should have dropped the price of the phone." Okay dropped it relative to what? "Obviously relative to last year's price." Why? There is/was heavy inflation and other products became more expensive but the iPhone didn't. At most you are complaining about shrinkflation.
Android users had/have(?) to side-load Fortnite. Depending on who you are that might feel like being "forced." Is your argument "If you feel like you are forced to use some app you are wrong and should just stop" or is it "If an app gets big enough that a lot of people feel forced to side-load it, then it earned the right not to abide by any platform holder policies."