Given an infinite amount of monkeys typing randomly on a typewriter for infinite time...

But they're typing for an infinite amount of time.

Surely you didn't miss that?

Depends on how many monkeys there are.

If there are countably infinite monkeys, then no.

If the number of monkeys is equal to or greater than the cardinality of the continuum, then yes.

Think of it this way: if every irrational number had a 100% chance of showing up, there would need to be at least that many monkeys to type each of those irrational numbers. So there would have to be more than countably infinite monkeys to match up with the irrational numbers.

does the typewriter have a pi symbol?

Infinity doesn't exist.

100%
every monkey will type 10 at least once
if you count in base pi

zero. Monkeys can't use typewriters

if it's a greek typewriter

Never, because the monkeys are typing, not writing.

If the whole floor was a keyboard, what exactly is the probably of squirrel typing down pi exactly?

1 out of Aleph_1

Logically speaking, I suppose that would depend on what you mean when you say "write down pi exactly" and what you mean by "monkey".

youtube.com/watch?v=V98soOyQWKY

The answer is 1.
If there is truly an infinite number of monkeys and infinite time.
Then somwhere on that infinite timeline pi will always be written.

I'd say that the odds are exactly pretty pretty good probably; the letter i is only one hop away from the letter p.

Not if there are countably infinite monkeys.

It depends on the what kind of infinity.

Proof:

P(A) = Possible Outcomes/Total outcomes

Possible outcomes:

A - Doesn't happen
B - Does happen

P(A) = 1/2

50% chance.

I still can't grasp the concept of aleph null and bigger infinities than infinity.
Infinity is infinity okay guys?

>infinite amount of mokeys typing randomly on a typewriter for infinite time
>a typewriter

Fuck you OP

>he doesn't have a natural affinity for concepts outside the practical boundaries and physically-grounded human brain like endless endlesses that are bigger than limitless limitlesses.

I don't think I'm supposed to kek.

I'd prove by induction but dont have a GED because I hated school.

unironically a brainlet

chances an ape eat my ass given a million dollar and three time limit

Trick question. Monkeys dont live forever.

i think that one of them typing "p, i" is pretty likely desu, at least 2/3

0% chance of anything meaningful come out of that due to the fact monkeys will just loop the same shit at the very best. Thinking they will have to type out the Library of Babel is just non-sense.

>Thinking they will have to type out the Library of Babel is just non-sense

If pi is a normal number they would HAVE to type out the library of babel at some point.

Probability is a function of knowledge. The more knowledge you have the more you can predict the future.

Your proof is "not" wrong, but it assumes that we don't know ANYTHING about the problem besides there are two options.

Since we actually know more about the problem than this, then the probability would not just be 50%, because probability depends on KNOWLEDGE.

Are you an idiot?

Are you an idiot?

>pi decimals continue infinitely
>probability of typing pi exactly

Zero. Even if all infinite monkeys were typing nothing BUT accurate pi digits for infinite time they would never finish and thus would not have written down pi exactly.

i choose to be ignorant to get more successful odds

checkmate

>that one autistic guy that can't conceptualize thought experiments

Imagine after 1 seconds the monkey types the first digit, after 1/2 seconds they type the second digit, after 1/4 seconds they type the third digit, 1/8, 1/16, etc etc.

After only 2 seconds the monkey would have written down every single digit of pi, all infinity digits. Boom.

Over time they'd evolve into humanoids, learn writing and typing and eventually develop geometry which would lead them to write down pi.

"Writes down exactly" implies that it will already be done, which is impossible since it takes infinite time. The probability that a monkey *is writing* down pi to infinite precision is 1.

Yes, which means they will never be done writing. So no monkey will have written down pi, but they will be writing down pi.

No, the monkeys hands and the typewriter would melt from the energy required to type that fast long before two seconds were up.

>I am literally incapable of thinking abstractly, don't mind me

Basically your though experiment is "If someone writes down the exact value of pi, they have written down the exact value of pi".

So now you have included supertasks which gives you infinite typewriters that can each print every real number, turning the initial question trivial

You completely misunderstood.

I am showing how the monkeys can finish in finite time.

Do I really have to think for you?

Only allow 2 seconds per typewriter.

That's not a monkey

"We've heard that a million monkeys at a million keyboards
could produce the complete works of Shakespeare;
now, thanks to the Internet, we know that it is not true."
– Robert Wilensky, UC Berkeley (1996)

user, you know that to prove this, you at least need to define the σ-algebra and the probability, right?

>Given an infinite amount of monkeys typing randomly on a typewriter for infinite time, what's the probability that one of them writes down pi exactly?

0%

they will all throw poop covered typewriters at eachother until they all die.

By specifying a new condition. Whereas OP implied they'd be typing at a somewhat constant rate.

Are you stupid? Typing faster doesnt get you closer to infinity. Thats how infinity works. Jesus this bait.

>an infinite amount of monkeys
>for infinite time
The probability is exactly 1 you dumbass