> The claim of the proof is that I=F(0)+F(π) is simultaneously positive and arbitrarily small, which is not possible for a fixed number, but totally possible if you see I as a sequence indexed by n.
This is not possible because I_n must be an integer for every n.
I conjecture that those of us who have taken exams entirely unprepared in the real world benefit from an immunity effect so that we never have to dream about it.
It should be blindingly obvious that a mask, any sort of mask, on a sick, coughing person acts to limit the quantity of infected sputum put into the air. Confusion arises on the right in particular because those guys simply cannot understand why they would wear a mask if the benefit is chiefly to other people.
I really wish it were first clarified in these discussions whether we are talking about benefit to the wearer or benefit to people around the wearer. The distinction appears to be completely absent both in the article and in the comments here on HN.
I think you are unjustified in squaring those numbers. A system that protects the borders protects the whole territory—so the relationship will surely be more linear than quadratic.
Yes. False beliefs breed more false beliefs, and at some point they catch up with us.
I had a colleague who was fanatically into soccer. I asked how does he feel when his team loses? It is devastating for many especially in big games. But he said he is willing to take the risk of rooting for a specific team and possibly losing because it gives him excitement. It's a bit like a drug really you get addicted to your team winning. It's a bit like any gambling addiction.
If you had no interest in the outcome of a soccer-match you wouldn't get very excited watching it.
In reality most people don't have a real interest in a soccer-game since they don't gamble money on it. Therefore it seems people pick a soccer-team to root for BECAUSE we want to get excited. We want that adrenaline. (or is it dopamine?) We want to believe that the arch of history tends towards our team winning.
False Belief 1: If my soccer-team wins I'll be much better off, much happier.
Consequent False Belief: Since my team did not win I must now be desolate. I must feel bad.
This is not possible because I_n must be an integer for every n.