Mark44 said:
Yes, this is different from saying 1/∞ = 0 which is a meaningless equation.
However, when we write limit n→∞1/n = 0 we're not saying that there is some n for which we get exactly zero. What we are saying, though, is this: however close to zero someone else requires, we can find a number N so that 1/n is closer than that required distance.
Ok yep. Aren't you also saying that 1/n is
never going to be zero and n is never going to be ∞?
PeroK said:
You should use the reply feature!
You have to be careful when a limit is meaningful. In this case, taking the limit as n→∞ does not result in a valid probability distribution. Technically, the limit is simply the zero function defined on the positive integers. And, the zero function is not a valid probability distribution.
Hm, if I'm understanding aren't you confusing the limit as n approaches infinity for the value of n which it definitely can never be? Doesn't the limit as n “approaches infinity” here result in a valid probability for n? If n= infinity it doesn't but if n=a jillion or a jillion gazillion etc. as in a limit "guess" calculation explained above doesn't it result in a valid probability for that guess?
If n= infinity you get 1/infinity for probability, more than one for sum of all probabilities both nonsense can't exist but best you can say is the limit as n approaches infinity is infinity which is fine however close it approaches the probability is just 1/that but n is never going to be infinity and 1/n never going to be zero.
So maybe all you can say is that a set with a
limit of an infinite of number of things exists thus it can't
actually have an infinite number of things and that the
limit of the probability of choosing a number is zero thus the
actual probability can never be zero. Maybe thus a set with an infinite number of things doesn't exist.
"If I talk about all the real numbers between 0 and 1 inclusive, I can indicate that by [0,1] or by . That is an infinite set."
I wonder if you did define a set maybe you just set boundaries or something. If you can't designate or enumerate separate things in the set do you have a set of things?
Maybe instead of saying all real numbers don't you have to say all real numbers down to 10^10 or 10^a jillion decimal places or something on and on because anything else is maybe not an actual definition of a set of things? Again, because the
limit of number of things in a set can be infinite but the number of things in the set can't actually be infinite?
You can sit down in a restaurant and soberly order an infinite number of hamburgers but they won't bring you anything they'll think you're crazy and can't pay for one because it's nonsense. Is that an actual legitimate order? But if you order a thousand hamburgers and are serious enough maybe with a briefcase full of money they might think the same but they'll at least recognize it as possible and explain they can't do it all they can do is 25 on short notice and then you say ok I'll settle for that.
But actually because of the “7%” inflation you really should just have one and you'll use a good portion of that briefcase on it.
Anyway I don't know if I'm able to argue any further than this I think I made my case maybe not I dunno.