/sci/ - Science & Math

>>12239697
>>12239733
Take the set of all rational translations (by rationals between 0 and 1) of the Vitali set. Fix an ennumeration of the rationals, and gradually remove translations. At any point, the set in the sequence still contains a translation of the Vitali set, so it has non-zero outer measure bounded below by the Vitali set's outer measure, but the intersection of all sets zeroes.

>get an email telling me to sign up for a PhD program in maths
>applications literally close tomorrow
>lads shouldn't even have my personal email
>it doesn't even make sense to send me that shit
>the program is from a subdepartment of one of my country's top three unis
>insititutional email, too
Did one of you somehow dox me and sent that as a joke?
>>11100942
Yeah.
>>11103222
>is there some key insight that I'm missing
Yes, but it's hard to explain. The function just passes through some point (possibly with a certain speed, etc) and then "goes with the flow." That is, the necessity of satisfying the equation "drags" the function around, even though bifurcations and the like might show up. Visualizing it physically in terms of a particle attracted by various forces is very convenient and recommended.
For ODEs, that is. This intuition largely becomes inconvenient for PDEs, except in some stuff like the method of characteristics.
>>11103349
The non-trivial ones.