/sci/ - Science & Math

Yes, yes it is, unless it was only creating integers.
Looking at 1 - 2
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
You are more likely to not get 1 or 2.

I would think you are most likely to get an irrational number. Unless your number generator can only make rationals.

>>1296655
Assuming this hypothetical generator existed then, how the fuck would it pick a number. There are infinite real numbers between any two integers, wouldn't any choice be impossible, since it is one possibility in infinite possible choices? Is this why a true random number generator is impossible?

i am confuse

A random *real number* generator is impossible.

>>1296671
It's like trying to pick a random number from 1 to infinity, it's impossible.

There are an infinite number of reals between any two reals. The odds of getting an integer: zero.

>>1296667
Stop trolling. Random number generators can only produce rational numbers.

>>1296632
If you had a computer which could deal with actual real numbers, than yes, the cardinality of the real numbers is greater than the cardinality of the whole numbers, and therefore you are infinitely more likely to get a non-whole number.

However, computers can't deal with the real numbers, they instead use a discrete floating-point notation to approximate the real numbers.

So if you had a true random number generator that could generate 64-bit floating points values between 1 and 10, then the likelihood of getting a whole number is not infinitely overshadowed by fractions. Knowing the number of bits used for the mantissa, exponent, and sign, it would be possible to precisely determine the probability. But I'm too lazy.

hey you guys. Say I flip a fair coin a few times and write down a 1 or a 0 depending on the outcome.
Say in the end I interpret these ones and zeros as a binary number.
Would that yield a normal distribution for the numbers 0 to 2^n - 1 where n is the number of coin tosses?

>>1296632
hey op look at it like this:

your chances of getting a number between 1 and 100 is 1%

your chances of getting a number between 1 and 1,000 is .1%

your chances of getting a number between 1 and 10,000 is .01%

your chances of getting a number between 1 and infinity are 0.000%

If you still dont understand what i mean, go to wikipedia and look up "Limited Infinities". Its basically saying that there are an infinite number of numbers between 4 and 5. Examples include 4.2, 4.89234, and 4.29884929348572398457209348570239485723098457293084769834567394856723098457230-94587923457623890457
9034567230945873892485678239084572394672390456734905687304956792034856792347562890345620394875623904
68739204856793458760239485673904587602394857603945876039458760394587630495876

do you see how that can go on forever?

Assuming your "true random number generator" just means the uniform distribution with support from 1-10, the probability of either a fraction or a whole number appearing is 0. The probability of an irrational number appearing is 1.

You might want to read this article on cardinality. It should explain to you how mathematicians compare the "size" of sets like the set of whole numbers or the set of numbers that can be represented as fractions.

http://en.wikipedia.org/wiki/Cardinality

>>1296708
well?

>>1296708
Or rather: what distribution would I get for those numbers?

>>1296708

No, it would yield a distribution where each whole number from 0 to 2^n - 1 has equal probability. That is nothing like a normal distribution.

>>1296740
>>1296730
/sci/: if it's not magnets, religion or preschool maths nobody will help you.

I am disappoint.

>>1296725
A computer capable of producing such random numbers as you describe is impossible. Digital computers can't calculate irrational numbers. It's like dividing by zero.

the probability of getting any number between 1-10 is 0.
p(x=0) = 0
p(x=3.24134524352) = 0

they are equally likely

Where are the fuckin' computer science majors?

>>1296708
guassian randomness is invariant under discrete convolution, so yes

>>1296763
P(x) = (1 / sqrt(2 * \pi * \sigma^2)) exp(-(x - \mu)^2 / (2 * \sigma^2))

It's still a gaussian or normal distribution.

>>1296842
<span class="math">P(x) = \frac{1}{sqrt(2 * \pi * \sigma^2)} exp(-\frac{(x - \mu)^2}{2 * \sigma^2})[/spoiler]

forgot the tags

>>1296842

Are you trolling me? Why did you type out the pdf of a normal distribution?

For one, a coin toss where you write 1 one heads and 0 on tails is not a normal distribution. It has two discrete outcomes. The normal distribution is continuous.

fun fact: almost surely, the number that appears has a decimal representation with more numbers than atoms in the universe

>>1296896
If you know that much, than you know the relationship between the normal and binomial distributions. Remember, we're not tossing it the coin once, we're tossing it <span class="math">n[/spoiler] times. The resulting distribution of values is a close enough approximation for a bounded normal distribution where the mean = 2^(N-1) and variance = 2^(2 * [N - 2]).

I actually should have used the bounded normal distribution density function, though, thanks for pointing that out.

The universe is the most complex possible computer that exists.

My brain is a program within this complexest of computers.

I pick the number 4 out of all possible and impossible numbers.

There. The truly random number is 4.

End thread.

>>1297117
Retard, your brain can only comprehend a limited range of numbers.