I just said "limits", and I didn't actually say anything about governments. I would not go as far as to say governments should force parents to have their children vaccinated, at least not for any current threats (if there were an extremely dangerous disease going around, with high likelihood of infection then maybe). Also, from what I've heard, governments often (usually?) do a horrible job of raising children.
I was actually addressing (as I thought the parent post was) the fact that the fundamental belief of Libertarians (of whom there are many in the US) is that self-interest trumps social interest. I was stating that I don't think this concept of "self-interest" can be applied to the vaccine issue in a clear-cut way. However I know that some Libertarians would say it does, because children have their parents' genes, and perhaps invoke Dawkins' "selfish gene" (I personally think this is a contrived pseudo-scientific argument and caring for a child has nothing to do with shared genes).
Except that I was counting non-mathematicians as well. A lot of people have difficulty grasping what is going on with 0.999... and what it means for that number to equal 1 (the idea that a number could have two representations in the same base goes over a lot of people's heads).
Yes, they do have difficulty. People who say that people who have trouble believing 1=0.999... are idiots are themselves having difficulty. 1 and 0.999... are different kinds of mathematical objects, hence in some sense they are not equal.
0.999... is not a "decimal expansion" of some number, but rather it denotes a sequence of numbers:
0.999, 0.9999, 0.99999,
The fact that "the real numbers can be defined as equivalence classes of Cauchy sequences of rational numbers" is probably not obvious to most of the people who think 0.999...=1 is obvious, and they would probably be surprised at how deep this area of mathematics is. See P-adic_number.
Also, one should not just casually accept the ideas of infinite series and sequences, because counter-intuitive things DO happen with them. There is no such thing as an "infinite decimal expansion" or "adding up an infinite number of numbers" -- those are just analogies, which may or may not mislead you in a given situation.
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