Varacca-Volzer computations

1449 days ago by Henryk

p = 0.5 for n in range(1,8): p = 0.5+0.5*p*p print "Probability of having antichain at depth " + str(n) + " is equal " + str(p) print "If no then we have measure 1, otherwise measure 0 :)" print "log_2(8)=3, hence 1/log_2^2(8) = 1/9" print 1-p >= 1/9 
       
Probability of having antichain at depth 7 is equal
0.836446540267109
If no then we have measure 1, otherwise measure 0 :)
log_2(8)=3, hence 1/log_2^2(8) = 1/9
True
k = 10. print 1/k-1/(2*(k**2)) print 1./log(2**k+1,2) print 1/(2*k)-1/(2*((2*k)**2)) >= 1./(2*log(2**k+1,2)) 
       
0.0950000000000000
0.0999859200388041
False
k = 2.**30 x = 2./log(k,2) print x-x**2/2 print 2./log(k+1,2.) print x-x**2/2 >= 2./log(k+1,2.) 
       
0.0644444444444444
0.0666666666636809
False
k = 2.**40 x = 1./log(k,2) print x-x**2/2 print 1./log(k+1,2.) print x-x**2/2 >= 1./log(k+1,2.) 
       
0.0246875000000000
0.0249999999999992
False