/sci/ - Science & Math » Thread #14100263

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Anonymous Fri 14 Jan 03:45:47 2022 No.14100263 View Reply Original Report

Quoted By: >>14100281 >>14100295 >>14100309 >>14100377 >>14100510 >>14102320 >>14102584

would a randomly chosen real number have an equal probability of being rational versus irrational?
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Anonymous

Anonymous Fri 14 Jan 2022 03:47:33 No.14100272 Report

Quoted By: >>14100305

No. The rational numbers are a subset of Lebesgue measure zero on the interval.

Anonymous

Anonymous Fri 14 Jan 2022 03:49:48 No.14100281 Report

Quoted By: >>14100290

>>14100263
what base? its different depending on if the base is prime, odd or even. 2 behaves like an even rare than a prime

Anonymous

Anonymous Fri 14 Jan 2022 03:51:18 No.14100290 Report

Quoted By:

>>14100281
It doesn't matter. All countable subsets of the reals have probability zero (what I was saying with "Lebesgue measure")

Anonymous

Anonymous Fri 14 Jan 2022 03:52:43 No.14100295 Report

Quoted By: >>14100305

>>14100263
"Randomly" is meaningless without specifying a probability distribution

Anonymous

Anonymous Fri 14 Jan 2022 03:55:20 No.14100305 Report

Quoted By: >>14100310 >>14100312

>>14100272
does that mean it's infinitely unlikely a random real number would be a rational number?
>>14100295
what about the distribution where all the real numbers are each equally probable?

Anonymous

Anonymous Fri 14 Jan 2022 03:56:42 No.14100309 Report

Quoted By:

>>14100263
Depends how the numbers are randomly generated. No dice or computer are going to be able to choose from all real numbers randomly. Almost none of them are even computable.

Anonymous

Anonymous Fri 14 Jan 2022 03:58:01 No.14100310 Report

Quoted By: >>14100316

>>14100305
>what about the distribution where all the real numbers are each equally probable?
Define it for me

Anonymous

Anonymous Fri 14 Jan 2022 03:58:13 No.14100312 Report

Quoted By: >>14100317

>>14100305
>does that mean it's infinitely unlikely a random real number would be a rational number?
Yes that's exactly what it means. In probability theory this is made rigorous

Anonymous

Anonymous Fri 14 Jan 2022 03:59:13 No.14100316 Report

Quoted By: >>14100322

>>14100310
Don't be a smartass, you're either a retard or you know what he means

Anonymous

Anonymous Fri 14 Jan 2022 03:59:19 No.14100317 Report

Quoted By:

>>14100312
okay cool. thanks.

Anonymous

Anonymous Fri 14 Jan 2022 04:00:33 No.14100322 Report

Quoted By: >>14100330

>>14100316
No, I want you to define a probability distribution on R for which all numbers are "equally probable"

Anonymous

Anonymous Fri 14 Jan 2022 04:01:42 No.14100330 Report

Quoted By: >>14100361

>>14100322
Not R, any finite interval on R. The uniform distribution on the interval. That's what he means

Anonymous

Anonymous Fri 14 Jan 2022 04:14:49 No.14100361 Report

Quoted By:

>>14100330
Okay if that's what he meant, then the question is obviously well-defined.

Anonymous

Anonymous Fri 14 Jan 2022 04:25:33 No.14100377 Report

Quoted By: >>14100482

>>14100263
No, you stupid goy.
The rationals are (((countably infinite))), whereas the (((irrationals))) are (((uncountably infinite))).

Anonymous

Anonymous Fri 14 Jan 2022 05:09:22 No.14100482 Report

Quoted By:

>>14100377
right. later I remembered this and felt kind of stupid. rationals are just riced up natural numbers they have the same cardinality.

Anonymous

Anonymous Fri 14 Jan 2022 05:16:49 No.14100510 Report

Quoted By:

>>14100263
You can't just randomly pick one. It has to be one or the other.

Anonymous

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Anonymous Fri 14 Jan 2022 16:59:59 No.14102320 Report

Quoted By:

>>14100263
literally impossible to select a random real number from among the real numbers. please learn 2 measure theory before you post here again.

Anonymous

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Anonymous Fri 14 Jan 2022 17:59:01 No.14102584 Report

Quoted By:

>>14100263
probability 1 because I randomly chose $7 \in \mathbb{Q}$

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