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Jun
28
asked What is the relationship of the Liar Paradox and Gödel's sentence?
Jun
12
comment What is the difference between Gödel's Completeness and Incompleteness Theorems?
Is there actually a name for a first-order-theory that is recursively enumerable, consistent and capable of arithmetic? If not, why not? Wouldn't that be a useful terminological distinction?
Jun
8
comment Are the Godel's incompleteness theorems valid for both classical and intuitionistic logic?
@PeterSmith I guess they refer to the infinite set of natural numbers. Would arithmetic on a set of natural numbers with a highest number (ultrafinitism) be complete?
May
20
comment Why are all the interesting constants so small?
Hm, it still doesn't fit quite since $2^{-2{^{2^{2^{2^{2^2}}}}}}$ is a small number. I think magnitude is a not good measure at all, but it's just about theorems that we are good at reasoning about. This alone doesn't explain why these numbers appear in widely different contexts, so this is where complexity comes into play.
May
20
comment Why are all the interesting constants so small?
I was aware of that problem when I wrote the answer. I'd guess now it's impossible to fully exclude the human context from an answer to this question. Short programs with exploding output are not interesting to us because we can't make sense of the resulting pattern. In a geometric interpretation the lines would go far beyond the field of view, or the dimensions would be too high. Ultimately, from a neurological view the result wouldn't fit into our working memories. So it's possibly only a one-way implication that explains it: Low complexity things that we understand, re-emerge all the time.
Apr
15
comment Why is integration so much harder than differentiation?
@spencer Haha, you are right. Thanks for the correction.
Apr
15
revised Why is integration so much harder than differentiation?
deleted 5 characters in body
Apr
14
awarded  Necromancer
Mar
29
awarded  Yearling
Feb
12
awarded  Popular Question
Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Mar
30
answered Examples of mathematical results discovered “late”
Feb
11
comment Does the central limit theorem apply for random variables with densities which are not asymptotic?
The normalization step is only for convenience (or even necessity) during calculation and proofs, right? And for increasing $n$ the variance converges to 0. Am I getting that right? How do we know it converges in a usable way (without a "detour")?
Feb
8
accepted What is the easiest and fastest way to produce a uniformly distributed random number between 0 and 9 off the cuff?
Feb
8
revised Does the central limit theorem apply for random variables with densities which are not asymptotic?
edited body
Feb
8
asked Does the central limit theorem apply for random variables with densities which are not asymptotic?
Jan
18
revised What is the easiest and fastest way to produce a uniformly distributed random number between 0 and 9 off the cuff?
added 11 characters in body
Jan
18
asked What is the easiest and fastest way to produce a uniformly distributed random number between 0 and 9 off the cuff?
Dec
17
revised Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?
Improved searchability of question title