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Originally posted by PhlabibitInfinite numbers? You never finish writing them on all the little bits of paper!
I'd take a bunch of numbers and throw them in a hat... I would also hope royalchicken had the skill to reach in said hat and remove a singe number......
Math that out!
Phla-
ps. More numbers?? Bigger Hat!
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Originally posted by FiathahelOK - But the resulting reals (in the 1/x and the tan example) are not evenly distributed. Therfore if you map the resulting real onto an integer you won't get an even distribution of integers. I'm not sure thats really a problem though, oh dear... 😕
You can also take any distribution of X on [0,1], and then look at 1/X
I am starting to feel there are no random numbers.
You could pick a number like 5.
or how about:
994, 873, 744, 838, 727, 776, 377, 484, 736, 226, 172, 838, 821
No one here can honestly say they ever saw that number before. And it still must be in the bottom .000000000000001 percent of all numbers possible.
What is the largest number you can think of? what is infinity minus one?
Ag.
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Originally posted by PhlabibitI quite like the method of tossing a stick, measuring the angle it's pointing at, normalising this to between -1 and 1, and interpreting the numbers after the decimal point as an integer. Does this give an equal (zero!) chance of picking any integer?
I am starting to feel there are no random numbers.
...
Ag.
Saying a number is random is nonsensical. Saying a number is "randomly selected from a set S" is meaningful, because a random selection is a function f:NxN-->S where f(m,n) = x means that the nth selection in the mth trial is x. This function must have thepropeties that P(x is selected) = P(y is selected) for all x,y in S. Furthermore, there must exist integers i,j such that for some n f(i,n) <> f(j,n).
A "random set of numbers" is just a set with some property occuring as frequently as pure probability would dictate.
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Originally posted by royalchickenPerhaps I was being a bit lazy, but by a random integer I did indeed mean a number randomly selected from the set of integers - isn't that the usually accepted meaning of my words? I also meant a "fair" randomly selected integer - as you put it:
Saying a number is random is nonsensical. Saying a number is "randomly selected from a set S" is meaningful, because a random selection is a function f:NxN-->S where f(m,n) = x means that the nth selection in the mth trial is x. This function must have thepropeties that P(x is selected) = P(y is selected) for all x,y in S. Furthermore, there must e ...[text shortened]... ers" is just a set with some property occuring as frequently as pure probability would dictate.
P(x is selected) = P(y is selected) for all x,y in the set of integers.
Originally posted by iamatigerIf you do it this way, the chance of picking any integer equals 0, cause most reals have infinite decimals and therefor do not represent an integer this way.
I quite like the method of tossing a stick, measuring the angle it's pointing at, normalising this to between -1 and 1, and interpreting the numbers after the decimal point as an integer. Does this give an equal (zero!) chance of picking any integer?
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Originally posted by FiathahelSigh - I think you are right. I thought the chance being 0 would not be a problem (the chance has to be 0 for any given integer in a workable method) but I suppose that if you take the digits of pi and try to interpret them as an integer then you can never work out even approximately, what the value of that integer is, so its not a particularly useful integer. In fact my method will never give you any integer with any determinable value.
If you do it this way, the chance of picking any integer equals 0, cause most reals have infinite decimals and therefor do not represent an integer this way.
Back to the drawing board! 😳
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Originally posted by royalchicken1
I don't think it is meaningful to talk of "selecting at random from a set" in terms of actual methods, because I challenge one of you to "randomly" select an integer from {1,2,3}.
(I just threw a dice until I got one of those numbers - only took 1 throw!)
Is that not a random enough selection for you?