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[Egan_BW]

Another nice one: if you pick a positive integer at random, what's the probability that it's prime?

Zero, because there's an infinite chance that your chosen integer will be infinite, and infinity can't be prime because it's not a number!
[trollface]

[heydude6]

Prime number theorem states the ratio of primes to composites, so the answer to your question is whatever that equation spits out. Sadly, the math is too complicated for me to read and understand.

[McTraveller]

I recently learned about n-adic numbers, and learned that infinities are just beyond normal comprehension.

Like how a number represented in base 10 as an infinite sequence of 9s is provably equal to -1, because if you add 1 to it, you end up with an infinite sequence of 0s. If you don't like that thought experiment you can do the thing like you do for repeating decimals; if m = ...9999999, then 10m = ....9999990, so m-10m = 9, so m(1-10)=9, so -9m = 9, so m = -1.

[pisskop]

Unreal numbers, man

[hector13]

I feel I should apologize for introducing mathematics to the wtf thread.

[Starver]

I feel I should apologize for introducing mathematics to the wtf thread.

It's a product of the additional power to divide us, 'cos the take-away from this is that we should just get real, log the sin and reciprocate with an equivalently base expression of vulgar irrationality.

[Mathel]

About the monkeys typing the word "bananas", it would actually be 9 separate keystrokes. Because in order for it to be a word, it has to have a space on each end. But the spaces can each be achieved through 3 different characters, those being LINE FEED, TAB, and SPACE.

Another issue is though, that they used the population of chimpazees. They should have taken the population of all monkeys, not just one species of apes.

[Frumple]

About the monkeys typing the word "bananas", it would actually be 9 separate keystrokes. Because in order for it to be a word, it has to have a space on each end

lodhavemercybutnoneodatistruahaha

[Starver]

About the monkeys typing the word "bananas", it would actually be 9 separate keystrokes. Because in order for it to be a word, it has to have a space on each end. But the spaces can each be achieved through 3 different characters, those being LINE FEED, TAB, and SPACE.

(Parentheses) "Quotes" :Other; ¿Hey? OrPresumeACamelCaseVariation.

Another issue is though, that they used the population of chimpazees. They should have taken the population of all monkeys, not just one species of apes.

Possibly bononononobos can type "banananananas" easier. (In both cases, easier to start than to stop!)


More seriously, this is all part of the "What actual parameters are they using?" question that I have. For example, if you did something like...

Code: (In Perl, but not actually tested for thinkos or typos) [Select]

while ($folio_text=~s/[^$valid]+//msg) {} # Strip any input not considered valid to actualy match
while ($chimp_text=~s/[^$valid]+//msg) {} # Strip anything not considered valid for match
&same($folio_text,$chimp_text) || next; # mismatch?
say "Yay!" && last; # success!
...then you could have it so that $valid="a-zA-Z" or $valid="\\w\\s" or $valid="\\p{ASCII}", but then they'd give totally different magnitudes when seeking emperical answers for how unlikely (or lengthy a wait) it would be for (a selection of) chimp texts to match the target folio text. (Equivalent for shielding off any 'awkward' keys on a mechanical typewriter.) Even more so if you also lc() or uc() it whilst pre-processing the string streams.

[MaxTheFox]

Prime number theorem states the ratio of primes to composites, so the answer to your question is whatever that equation spits out. Sadly, the math is too complicated for me to read and understand.

You can switch to Simple English in the language menu for complex technical articles to get a quick run-down. https://simple.wikipedia.org/wiki/Prime_number_theorem

The prime number theorem is a theorem from number theory. Prime numbers are not distributed evenly across the number range. The theorem formalizes the idea that the probability of hitting a prime number between 1 and a given number becomes smaller, as numbers grow. This probability is about n/ln(n), where ln(n) is the natural logarithm function. This means that the probability of hitting a prime number with 2n digits is about half as likely than with n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (ln 101000 ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (ln 102000 ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly ln(N).[1]

Fifteen-year old Carl Friedrich Gauss suspected that there was a link between prime numbers and logarithms in 1793. Adrien-Marie Legendre also suspected such a link in 1798. Jacques Hadamard and Charles-Jean de La Vallée Poussin proved the prime number theorem in 1896, over a century after Gauss.

[NJW2000]

Another nice one: if you pick a positive integer at random, what's the probability that it's prime?

Zero, because there's an infinite chance that your chosen integer will be infinite, and infinity can't be prime because it's not a number!
[trollface]

This gave me a small headache, which I assume was the intention.

Prime number theorem states the ratio of primes to composites, so the answer to your question is whatever that equation spits out. Sadly, the math is too complicated for me to read and understand.

This is a pretty good answer. The theorem in question tells you that for a big enough number N, the proportion of primes under N tends to be close to1/log(N). As N tends to infinity, 1/log(N) approaches 0, so the chance of picking a prime at random from all integers is 0.

Was this roughly your thought process?

You’re not exactly wrong - this is definitely AN answer. But you’re not exactly right either.

You’d be just as right if you’d said 0.5, in fact.

[MaxTheFox]

Actually, in statistics there is the concept of "almost all" or "almost none".

Say you have an infinite set A where there are an infinite amount of 1s but, say one or two or a thousand 2s. Intuition says that you have zero probability of picking a 2 if you randomly picked an element. But actually you have an almost zero probability of picking a 2. So, 0 for practical purposes but for some mathematical functions the distinction matters.

Mathematicians are a pedantic bunch.

[pisskop]

So what I'm getting out of all this is that somewhere in between my grade 7 algebra II and Quantum Statistics there is a useful application of math?

[Eschar]

Another nice one: if you pick a positive integer at random, what's the probability that it's prime?

Zero, because there's an infinite chance that your chosen integer will be infinite, and infinity can't be prime because it's not a number!
[trollface]

There's zero chance of your chosen integer being infinity because it's not an integer

[Starver]

There's zero chance of your chosen integer being infinity because it's not an integer

Indeed. It's a fruit, even though people usually tend to treat it as a vegetable.