/sci/ - Science & Math

[Anonymous No.10035215]

If your domain is all real numbers what is the chance of picking an integer?


Is it zero?

Or is it 100%

Somewhere in between ??

[Anonymous No.10035233]

>>10035215
Almost all of the numbers are irrational so it's zero.
Proof: Think

[Anonymous No.10035234]

>>10035233
But there are also infinite integers

[Anonymous No.10035245]

>>10035215
Why aren't integers considered "real numbers"?

For example:

1.000...

[Anonymous No.10035257]

>>10035245
The set of integers is a subset of real numbers. As such, they are real numbers.

[Anonymous No.10035259]

>>10035234
See: Measure theory and/or probability theory for why this is the case.

[Anonymous No.10035264]

>>10035257
Is 1.000... a whole number?

[Anonymous No.10035269]

>>10035264
Great question, what do you think yourself?

[Anonymous No.10035270]

>>10035234
Imagine a domain of multiples of 1/3. It would look something like; ... -0.666.., -0.333.., 0, 0.333.., 0.666.., 1, 1.333.., ... Now imagine if you were to randomly pick any number from this domain. What are the chances of picking an integer if there are two non-integer rational numbers for every integer?

[Anonymous No.10035272]

>>10035215
You can't pick a radom number if the cardinality of the set you pick from is not finite.

[Anonymous No.10035276]

>>10035269
The value is exactly the same to '1', so if it is a whole number, it means zero is not a number.

[Anonymous No.10035328]

>>10035272
>>10035276
>t. Brainlets

If your variable's domain is an interval then it it continuous on that interval and you need to use the lebesgue measure to measure your probabilities (integrals). The Lebesgue measure of an interval [a,b] is given by L ([a,b])=b-a so the measure of any "number" x is L ([x,x])= x-x = 0, meaning that the probability of your variable being equal to any number is 0 as long as your variable is continuous.

[Anonymous No.10035341]

>>10035215
>If your domain is all real numbers what is the chance of picking an integer?
so are you talking about a probability density function? if so then it depends on the function. If you allow discontinous functions you could have something like

f(x) = delta(x - 1)*0.5 + any function with integral equal to 0.5

[Anonymous No.10035342]

>>10035215

I'm a sick fuck I like a quick fuck

[Anonymous No.10035376]

>>10035328
Apply this to 1.000...

[Anonymous No.10035384]

>>10035215
wtf why is this stickied

[Anonymous No.10035385]

>>10035215
The probability is 0

How?? Just read this free guide https://en.m.wikipedia.org/wiki/Almost_surely

[Anonymous No.10035452]

>>10035328
the lebesgue measure is not a probability measure
your intuition is fine but you need to think about what kind of probability measures you can define on R

also
>If your variable's domain is an interval then it it continuous on that interval and you need to use
wtf is this nonsense nigger

[Anonymous No.10035486]

>>10035452
Nigga wtf the probability measure is just the integral of the density with respect to the lebesgue measure in the continuous case. If the lebesgue measure is equal to 0 the probability measure is equal to 0.

Also nigga if the domain is an interval then the algebra you use has to be the Borelian one therefore your variable is continuous. If it is discrete or neither continuous nor discrete your domain is not an interval and the measure is no longer the lebesgue one. Literally Probability 1 shit

[Anonymous No.10035890]

>>10035215
50%, either you pick an integer or you don't.

[Anonymous No.10036692]

>>10035233
Since Q is dense in R wouldn't the probability of getting an irrational be 50%?

[Anonymous No.10036811]

Z has cardinality aleph naught, R has the cardinality 2^aleph naught or aleph 1 if the continuum hypothesis is true.

Figure it out from here tards.

[Anonymous No.10038235]

>>10035233

FPWP. The OP never specified that a number from among the reals is to be picked AT RANDOM, though this is the common, lazy, natural-language interpretation. That's not what the OP actually says though. It only says to somehow pick a number from among the reals, leaving it up to the reader to determine how.

Given this, any of the OP's three suggested possibilities may be the answer, given the choice of rule or function for what to pick (only pick integers, only pick non-integers, randomly pick, use some other rule...)

[Anonymous No.10038309]

Most "real numbers" aren't real, so it is calculable, and something in-between. I think there are at least three more cases of real numbers besides those given by radicals, but that is very, very hard to prove. Open question.

[Anonymous No.10038311]

>>10038309