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May
20
accepted Prove limit doesn't exist using epsilon-delta defintion
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
Well, Turing's universal computation thesis implies that if someone as mathematically challenged as myself can (and is expected to) apply a procedure to solve this problem (I'm supposed to learn, i.e. to develop a pattern of dealing with similar problems!), then a digital computer should too! :) Anyways, this wasn't said in all seriousness! I very much value your time and effort you put into answering his, hence, I'll accept your answer, even though I don't feel content with it. :)
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
Not arguing, but how do systems like Maple, Mathematica or Maxima solve limits? I'm sure they use heuristics too. But maybe there are some restrictions for the problem which make some subset of it decidable? After all, there are lots of everyday things in computer science, which are undecidable, yet they are used on a regular basis in mission-critical systems.
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
To be more concrete: here you use the "trick" which allows you to avoid slow-but-sure calculation when you substitute value for $\lfloor sin x \rfloor$ because you know how the function behaves at the entire range $(-\sigma, \sigma)$, but a computer wouldn't know that and isn't allowed to assume this based on few values it can compute, thus it wouldn't be a permissible slow-but-sure approach.
May
20
revised Prove limit doesn't exist using epsilon-delta defintion
added 554 characters in body
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
Yes, but that doesn't help. I need to know what and if did I do wrong.
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
Sorry for extensive commenting, maybe this'll explain it better. Compare these: say, you could multiply matrices by recognizing that one of the matrices is diagonalizable and so you could simply use the eignevalues for multiplication (which would be quicker), or you could ignore that fact and just do the slow-but-sure row-by-column multiplication. I'm certain there's a slow-but-sure way to solve any limit problem, and that's what I'm trying to find. (Unfortunately, my teacher and the textbooks are worthless at that).
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
I just need the very superficial, algorithmic, if you like, way to approach solving this kind of problems. I don't have a problem seeing why this limit doesn't exist. I plotted it, and made sure I completely understand how the function behaves etc. My problem is with the specific way of solving the problem, not with solving it in general (if I just wanted to solve it, I'd simply typed it into Maxima or Maple and be happy with the result).
May
20
revised Prove limit doesn't exist using epsilon-delta defintion
added 33 characters in body
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
I probably need to explain more. Since I'm just learning this, I'm struggling with finding a general procedure for solving such problems, so I would really like to either solve it using the way I stared, or to find out that the way I attempted to solve was wrong. Alternative answers, which use some unique property of this formula are great, but I would appreciate it, if the answer was dealing with the specific way of solving the problem.
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
@RobArthan yes, I do mean floor. I typoed the first time I wrote it. And yes, I have all reasons to believe it should be simple, and yet I'm asking this question.
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
Sorry, I just now realized I typoed when I wrote the initial formula. Sorry. And, yes, I know the limit of sine of x divided by x, but that's not really helping because I need a specific way of proving it, not just any way, and I have problems with that particular way.
May
20
revised Prove limit doesn't exist using epsilon-delta defintion
A very important typo!
May
20
comment Prove limit doesn't exist using epsilon-delta defintion
I bet I would if I knew how, but thanks for trying :)
May
20
asked Prove limit doesn't exist using epsilon-delta defintion
May
15
accepted Number of permutations of a string with consequtive repetitions disallowed
May
15
comment Number of permutations of a string with consequtive repetitions disallowed
Oh, thanks! I see now, I was even closer to this solution than you can see in the one I posted. Where I went wrong by assuming I need to count the "internal arrangements" of $AAA$ when I'm counting all strings containing $AAA$, not the "remaining doubles".
May
15
asked Number of permutations of a string with consequtive repetitions disallowed
Apr
30
comment What are numbers?
@mweiss oh, I see now, weird it didn't come up in the search. math.stackexchange.com/q/865409/856 this one has some very good answers.
Apr
30
comment What are numbers?
I too thought about Wittgenstein right away! Actually, I've started pondering this question here: cs.stackexchange.com/questions/41956/… but then decided that it's more appropriate in this forum.