[eriksank]

I suspect that such program could revolve around showing that for any arbitrarily small number -- almostZero -- you can always find two smaller numbers x1,x2 as such that sin(1/x1) is smaller and sin(1/x2) is larger than sin(1/almostZero). The Popper-compliant claim could be: find me an almostZero for which the defeating function will be incapable of producing such x1 and x2. I am not sure about all of this, though. Unless you have investigated something very similar before, it takes time to investigate things like that.