/sci/ - Science & Math

I see ya boy has published something again, after several years, last year

https://arxiv.org/pdf/2002.04703.pdf

That episode where Nelson posted the paper on the inconsistency of PA and Terence Tao finds an error on it is actually online, with the two interacting, in the nlab blog page

https://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html#c039547

iirc Nelson was actually the logic Prof of Tao.

From my understanding, to his death he was quite sure to be able to prove that some computational complexity argument about PA would actually not work out since to express them you need PA and they say something about (recursively defined) numbers that you don't have available yet, at the stage about which you make arguments. Something like that.

>>12423749
https://en.wikipedia.org/wiki/Dual_number#Linear_representation

I think if k is the amount you have, and P is the probability to go up and 1-P is the one to go down, then the probability for the change [math]\Delta k[/math] is

[math]\Delta p(k, \Delta k) = P\, \delta_{\Delta k, 1} + (1-P)\, ( \delta_{\Delta k, -1} + \delta_{k, 0} (\delta_{\Delta k, 0} - \delta_{\Delta k, -1})) [/math]

At time n=0, you start with

[math] p(k,n=0) = \delta_{k,0} [/math]

money and each time step follows from the last one by integrating over the steps (+1, 0, -1).