this post was submitted on 08 Dec 2024
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The whole point is that one of the terms has to be infinite. But it also works with infinite number of monkeys, one will almost surely start typing Hamlet right away.
The interesting part is that has already happened, since an ape already typed Hamlet, we call him Shakespeare. But at the same time, monkeys aren't random letter generators, they are very intentional and conscious beings and not truly random at all.
This is guaranteed with infinite monkeys. In fact, they will begin typing every single document to have ever existed, along with every document that will exist, right from the start. Infinity is very, very large.
no, it is not. the chance of it happening will be really close to 100%, not 100% though. there is still small chance that all of the apes will start writing collected philosophical work of donald trump 😂
It's not close to 100%, it is by formal definition 100%. It's a calculus thing, when there's a y value that depends on an x value. And y approaches 1 when x approaches infinity, then y = 1 when x = infinite.
it is not
you weren't paying attention in your calculus.
y is never 1, because x is never infinite. if you could reach the infinity, it wouldn't be infinity.
for any n within the function's domain: abs(value of y in n minus limit of y) is number bigger than zero. that is the definition of the limit. brush up on your definitions 😆
Except, that's in the real world of physics. In this mathematical/philosophical hypothetical metaphysical scenario, x is infinite. Thus the probability is 1. It doesn't just approach infinite, it is infinite.
oh boy, no. if anything, it would be the other way around. in real world calculations, you can sometime approximate and still get reasonably precise result, or boundary, depending on your needs. not so in math.
hence the jokes like "for mathematician, pi as a pi. for physicist, pi is roughly 3,14, for civil engineer, pi is roughly 3."
it is not.
x is not infinite. x is a variable, that is to be substituted by specific number. infinity is not a number, it is a concept that express the fact that you explore how the function behaves when you are substituting bigger and bigger numbers. but none of these numbers are "infinity". it is always specific number and the result never reaches the limit of the function. in this case, it is never 1, no matter how big number you substitute.
https://en.wikipedia.org/wiki/Limit_of_a_function