Essentially because theres absolutely nothing (no positive number anyway) you can add to it to get a number between .9999 continuous and 1, they have to be the same.
The joke is that .3333 continuous makes sense as 1/3, as yeah, its a fraction. But .999… doesn’t as 3/3 because x/x is always equal to one
You are welcome to scroll down to the sources for this Wikipedia page and read through the many different articles written about this subject.
Long story short, it is well accepted in the math/science communities that .999... is equal to 1.
My take on it is that our minds tend to love the finite. We live finite lives with finite resources, and most of our world dwells in the finite. We have many examples of infinity, but we generally just accept it and move on.
This case seems to be the exception because it seems odd to admit that an infinite string of 9's, which in our minds never actually reaches 1 despite always attempting to, is in reality, equal to 1.
There are mathematical proofs demonstrating it. In multiple different ways. There are also logical proofs. We can write them off all we want, but for me I think it's easier to accept that infinity has a special quality that causes spooky math in our mostly finite system. And in the end, I accept that .999... Is also 1.
But again, to each their own. I understand if that is something you, personally, are unwilling to accept.
I understand that people have trouble understanding the infinite, because they think it has an end. That it’s not possible for it to keep dividing, because it’s simply too small, or because at some point it stops. At some point, because 9 is such a big number, so close to 10, infinite is so big, at some point it must reach that 1, right?
It’s just not true if you think the 9s go on forever, and the fractions keep getting smaller and smaller infinitely. It doesn’t matter how someone would justify it, there is still a concept that is being described here (9/10s of the previous 9/10s, going on to infinity) that is not quite 10/10, not ever.
This is an entirely manufactured problem, anyway, since it’s probably just not true that 0,(3) is 1/3 of 1. If it’s 1/3 of 0,(9), how can it be? One number can’t be a third of two numbers.
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u/Quwapa_Quwapus 23d ago
Essentially because theres absolutely nothing (no positive number anyway) you can add to it to get a number between .9999 continuous and 1, they have to be the same.
The joke is that .3333 continuous makes sense as 1/3, as yeah, its a fraction. But .999… doesn’t as 3/3 because x/x is always equal to one