I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
this post was submitted on 06 Jan 2024
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There is an infinite amount of possible values between 0 and 1. But factorially it means measuring a coastline will lead towards infinity the more precise you get.
And up all the values between 0 and 1 with an infinite number of decimal places and you get an infinite value.
Or there's the famous frog jumping half the distance towards a lilly pad, then a quarter, than an eighth. The distance halfs each time so it looks like they'll never make it. An infinitesimally decreasing distance until the frog completes an infinite number of jumps.
Then what most people understand by infinity. There are an infinite number of integers from 0 to infinity. Ultimately this infinity we tend to apply in real world application most often to mean limitless.
These are mathematically different infinities. While all infinity, some infinities have limits.
Yes! The difference between these two types of infinities (the set of non-negative integers and the set of non-negative real numbers) is countability. Basically, our real numbers contain rational numbers, which are countable, and irrational numbers, which are not. Each irrational number is its own infinity, and you can tell this because you cannot write one exactly as a number (it takes an infinite numbers of decimals to write it, otherwise you've written a ratio :) ). So, strictly speaking, the irrational numbers are the bigger infinity between the two.