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i want a mathematical definition of randomness. since i don't think a -ness word is commonly (or perhahps ever) defined in math, maybe it'd be better to define random. since random is more like an adjective, how about a random blah where blah could be at least these three things: sequence or variable or number

so let's just ask these questions:

what is a random sequence?

what is a random variable?

what is a random number?

and if you want

what is a random event?

if you don't mind, state your opinion (w or w/o proof) that:

1. random sequences exist (or not), how many there are, and how to decide if a given sequence is random.

2. random variables exist (or not), and how to decide if a given variable is random.

3. random numbers exist (or not).

4. random events exist.

what i'm ultimately wondering is whether no, any, or all events in the universe are random though if you thought i meant event in the statistical sense that's ok. i don't really expect my questions to address what i'm ultimately wondering without undertaking what may be a logical leap of extrapolating math to philosophy/science (eg that it can't be decided if a given sequence is random then it can't be decided that a given event is random).

incidentally, if you were to pick a random real number, what is the probability that it is less than x (where x is in R)? how about between -x and x? i think the answer to this question ought to be 0 even if x=googleplex

so let's just ask these questions:

what is a random sequence?

what is a random variable?

what is a random number?

and if you want

what is a random event?

if you don't mind, state your opinion (w or w/o proof) that:

1. random sequences exist (or not), how many there are, and how to decide if a given sequence is random.

2. random variables exist (or not), and how to decide if a given variable is random.

3. random numbers exist (or not).

4. random events exist.

what i'm ultimately wondering is whether no, any, or all events in the universe are random though if you thought i meant event in the statistical sense that's ok. i don't really expect my questions to address what i'm ultimately wondering without undertaking what may be a logical leap of extrapolating math to philosophy/science (eg that it can't be decided if a given sequence is random then it can't be decided that a given event is random).

incidentally, if you were to pick a random real number, what is the probability that it is less than x (where x is in R)? how about between -x and x? i think the answer to this question ought to be 0 even if x=googleplex

^{googleplexgoogleplex}
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