Nikita Danilov

Too like the lightning, which doth cease to be / Ere one can say 'It lightens'.

[Nikita Danilov @nikitadanilov]

@alz_zyd_ Berkeley rightly laughed Newton for this.

[Nikita Danilov @nikitadanilov]

@audvin @dannyconversano @haider1 Newtonian mechanics, special and general relativity and quantum mechanics (these four are basically the entire scope of progress in physics in the last 400 years) were created without any engineering feedback.

[Nikita Danilov @nikitadanilov]

@LongFormMath The condition that p_n is prime is never used after the first inequality, so the theorem holds for any sequence satisfying that inequality.

[Nikita Danilov @nikitadanilov]

@getjonwithit Construction of T equivalent to L(# T) > n is exactly a diagonalisation.

[Nikita Danilov @nikitadanilov]

@tsoding Now do "MOV (PC)+, (PC)+". :-)

[Nikita Danilov @nikitadanilov]

@Anthony_Bonato \chi is overrated.

[Nikita Danilov @nikitadanilov]

@gammaofzeta There is a construction of reals in line with structure (and simplicity) of rationals and integers. Search for "Eudoxus reals"

[Nikita Danilov @nikitadanilov]

@DrDavidVernon I beg to differ. :-)

[Nikita Danilov @nikitadanilov]

@AmericanGwyn @leach_leach That must be the Hungarian National Soccer Team in the background.

[Nikita Danilov @nikitadanilov]

@eatonphil emacs + wgrep mode.

[Nikita Danilov @nikitadanilov]

@PulkkinenEsa @MaszynaTrurla @Anthony_Bonato But here the sequence of definitions does make sense from a categorical point of view: a groupoid is a category where each morphism is isomorphism, and a group is a groupoid with one object.

[Nikita Danilov @nikitadanilov]

@sarah_zrf We were doomed when Fibonacci imported big-endian numerals from a right-to-left writing culture into the left-to-right one.

[Nikita Danilov @nikitadanilov]

@PhilosopherJoeC @DrJavierDeLaHe1 PA defines arithmetical terms and formulae. "True" means provable. 1+1=2 is provable. Truth of a Godel statement is also proved (specifically, in the Godels's paper).

[Nikita Danilov @nikitadanilov]

@JDHamkins position. After this substitution, the string looks like PrrrX, where P is never modified. So by the lemma, Prr will be never modified after that point. Now we have a shorter string rX with an infinite history.

[Nikita Danilov @nikitadanilov]

@JDHamkins this substitution the string looks like PrruuuY, so by the inductive assumption, Prruu and hence Prr will never be changed. QED. Now for an arbitrary infinite history, take the leftmost ever substituted triple, say PludX. Then find the earliest substitution in this [position]

[Nikita Danilov @nikitadanilov]

@_ryanruby_ @FCardamenis Anna Karenina surely. She was supposed to be an exemplary fallen woman, before Leo fell in love with her.

[Nikita Danilov @nikitadanilov]

@taz_chu Gower's "general statement" is also wrong: take empty X.

[Nikita Danilov @nikitadanilov]

@tavianator @mulltuhh @dnspies @imperialauditor X is not the domain, it's an individual.

[Nikita Danilov @nikitadanilov]

@JDHamkins Isn't ZF hierarchy not really a hierarchy, because a level in it can contain sets definable only through comprehension of a formula with parameters from higher levels? That is, it's impredicative?