Random Integer

Originally posted by Phlabibit
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!

Infinite numbers? You never finish writing them on all the little bits of paper!

Originally posted by Fiathahel
You can also take any distribution of X on [0,1], and then look at 1/X

OK - 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... 😕

Another example:
X=0
Flip a coin: if head increase X by one and flip again. If tail, stop.

Originally posted by Fiathahel
Another example:
X=0
Flip a coin: if head increase X by one and flip again. If tail, stop.

Still rather biased towards the lower integers...

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.

Originally posted by Phlabibit
I am starting to feel there are no random numbers.

...
Ag.

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?

what is the biggest number you could write at RHP before you get a [Word too Long] error???

Phla-

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.

Originally posted by royalchicken
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.

Perhaps 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:
P(x is selected) = P(y is selected) for all x,y in the set of integers.

Originally posted by iamatiger
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?

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.

Originally posted by Fiathahel
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.

Sigh - 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.

Back to the drawing board! 😳

Originally posted by royalchicken
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}.

1
(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?

Originally posted by iamatiger
1
(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?

In theory it is possible to determine on the basis of classical physics what the outcome of a dice throw will be.

Originally posted by royalchicken
In theory it is possible to determine on the basis of classical physics what the outcome of a dice throw will be.

... and what about if the "dice" is a computer program ?

The same. Pseudorandom numbers are deterministic. A few physical processes give pseudorandom numbers tht pass statistical tests with very high marks, but true "randomness" is really a statistical ideal.