So, that episode's on right now. How would you even go about quantifying the odds of rolling a number on the infinity-sided die? It's a fun little thought. I love math stuff. owo
So, that episode's on right now. How would you even go about quantifying the odds of rolling a number on the infinity-sided die? It's a fun little thought. I love math stuff. owo
The question is, is that really the case? I was discussing this with my cousin and one of my math professors and I came upon this logic. First of all, if you didn't know, there are two types of infinity: countable and uncountable. Sparing you the details, rational numbers are a countably infinite set and irrationals are uncountably infinite. And by their nature, there exist infinitely more irrational numbers than rational numbers. So if I were to pick a numbers at random of all the numbers in existence, the probability of pulling an irrational number is effectively 100%.
So with similar thinking, I figure it's fair to consider that you can assign a natural number to each of the infinite non-number events. If that's possible, then there is a countably infinite number of non-number events. This is versus the uncountably infinite set of all real numbers (not to mention imaginary and complex).
So by that, I argue that there is effectively a 100% chance of rolling a number rather than triggering an event. Granted, there's technically a chance of and non-number event happening, but it's an infinitely small chance, being effectively zero.
I like math. owo
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When there is two different variables (here events and numbers) there cant be 100% of anything just saying
That's where the term "effectively" comes into play. What I presented up there claims that there are infinitely more numbers than there are non-numbered events. If you take the limit of a/x as x approaches infinity, where a is some positive constant, you get zero. Technically, it never reaches 0, but it keeps getting closer and closer. So "at" infinity (you can never get to infinity as it's just a concept), you're looking at a number that's infinity small but still have value. (An infinitesimal is what this is called.) So there's an infinitely small chance that you can roll a non-number, but there's a 99.99999999999999999...% chance of rolling a number. (For the record, if you write 99.99999... as a rational number, it's 100.)
So I'm claiming the number of numbers dwarfs the number of non-numbers by this extreme. Basically, Ford got an extremely lucky roll in that episode such that he had an infinitely small chance within an infinitely small chance to bring those characters to life.
Of course, there are concepts in mathematics that I don't know like measure theory, which might apply here, so I could be off a tad.
Also, just some quick math to clarify something I mentioned up there, let .9999...=x. Then 99.999....=100x. (Since the nines go off infinitely, you don't lose any decimal places.) So 100x-x=99 which means 99x=99 which means x=1. So .999999...=1 making 99.9999....=100.
Though now I'm talking with my math professor on Facebook and he's trying to explain to me why it would be a 0% probability instead. @.@
I love math, but sometimes theory stuff gets super confusing. xD;;