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visits member for 2 years, 11 months
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Dec
14
comment Invariants that might determine graph up to isomorphism
re HS comment, it would be good if the author of the paper updates it to state the error and extract anything else useable from the framework. otherwise there may be further questions
Oct
22
awarded  Nice Answer
Sep
24
awarded  Autobiographer
Aug
27
awarded  Informed
Aug
26
comment Do the base 3 digits of $2^n$ avoid the digit 2 infinitely often — what is the status of this problem?
Tao (end of blog post) cites some refs & draws some analogy to the collatz conjecture. apparently Erdos conjectured "2" always appears in the base-3 expansion for all $i>8$
Aug
21
comment Collatz property implying infinite “fall below” trajectories, is it known?
Aeryks formulation is what is intended, thx for that (mea culpa for not initially rigorously stating it). have worked with "backwards" algorithms like what AlexR refers to but dont know what mathematical form the sets take, have to think about that more, dont see how to derive the above property that way. (note property is implied by Collatz conjecture.)
Aug
21
comment Collatz property implying infinite “fall below” trajectories, is it known?
the "fall below" property is interrelated but not exactly the same as the "terminates at 1" property. the conjecture is also true iff all trajectories "fall below". but a "fall below" property of a trajectory does not nec(?) guarantee it terminates at 1. (by induction) a "fall below" trajectory does terminate at 1 if all trajectories starting below it also have the "fall below" property. here "full trajectory" means a trajectory ending at 1.
Aug
20
asked Collatz property implying infinite “fall below” trajectories, is it known?
Aug
14
comment Examples of unexpected mathematical images
also see eg Phase Plots of Complex Functions: a Journey in Illustration / Wegert, used to visualize the Riemann zeta fn & related ones
Aug
11
answered Examples of unexpected mathematical images
Aug
4
comment Prime factorization “demoted” leads to function whose fixed points are primes?
what app did you use to generate the graph?
Aug
4
comment Prime factorization “demoted” leads to function whose fixed points are primes?
some superficial resemblance to collatz conjecture in the iteration etc. there is some way of unifying these types of questions under an automata theory formulation.
Jul
19
comment Negative impact of wrong or non-rigorous proofs
the question is slightly leading. any erroneous theorem or lemma anywhere leads to "0=1" elsewhere. it can be very timeconsuming for others to discover/find these "defects" (there is some loose analogy to software engineering). so "damage" is an overwrought/dramatic word/adjective in this context. but, ofc, "to err is human..." even by professional mathematicians. agreed that fixing errors can lead to highly constructive new math/research etc.
Jun
9
comment Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prerequisites? Good introductory texts?
did anyone cite the wikipedia article?
Jun
6
comment Mistakes in mathematics, false illusions about conjectures
nice question but dislike the vagueness of the initial paragraph. why not cite the example? sounds like you could be referring to an important open problem...
May
30
revised Is it easy to produce hard-to-color graphs?
added 61 characters in body
May
30
answered Is it easy to produce hard-to-color graphs?
May
30
comment Is it easy to produce hard-to-color graphs?
suggest migrate to Theoretical Computer Science. the questions are closely connected with P=?NP conjecture.
May
7
comment Examples of mathematics motivated by technological considerations
noticing many refs from TCS below. so see also eg core algorithms deployed tcs.se
May
7
comment Interesting examples of generic behavior of mathematical objects being either unreasonably structured or simply unreasonable
alas interesting idea but probably too broad when undecidable problems are taken into acct (undecidability is quite rampant). also, fractals. also, Collatz conjecture related to integer iterative/dynamic equations.