794
I just cited myself.
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No, it equals 0.999...
2/9 = 0.222... 7/9 = 0.777...
0.222... + 0.777... = 0.999... 2/9 + 7/9 = 1
0.999... = 1
No, it equals 1.
Sure, when you start decoupling the numbers from their actual values. The only thing this proves is that the fraction-to-decimal conversion is inaccurate. Your floating points (and for that matter, our mathematical model) don't have enough precision to appropriately model what the value of 7/9 actually is. The variation is negligible though, and that's the core of this, is the variation off what it actually is is so small as to be insignificant and, really undefinable to us - but that doesn't actually matter in practice, so we just ignore it or convert it. But at the end of the day 0.999... does not equal 1. A number which is not 1 is not equal to 1. That would be absurd. We're just bad at converting fractions in our current mathematical understanding.
Edit: wow, this has proven HIGHLY unpopular, probably because it's apparently incorrect. See below for about a dozen people educating me on math I've never heard of. The "intuitive" explanation on the Wikipedia page for this makes zero sense to me largely because I don't understand how and why a repeating decimal can be considered a real number. But I'll leave that to the math nerds and shut my mouth on the subject.
My brother. You are scared of infinities. Look up the infinite hotel problem. I will lay it out for you if you are interested.
Image you are incharge of a hotel and it has infinite rooms. Currently your hotel is at full capacity... Meaning all rooms are occupied. A new guest arrives. What do you do? Surely your hotel is full and you can't take him in... Right? WRONG!!! You tell the resident of room 1 to move to room 2, you tell the resident of room 2 to move to room 3 and so on.... You tell the resident of room n to move to room n+1. Now you have room 1 empty
But sir... How did I create an extra room? You didn't. The question is the same as asking yourself that is there a number for which n+1 doesn't exist. The answer is no... I can always add 1.
Infinity doesn't behave like other numbers since it isn't technically a number.
So when you write 0.99999.... You are playing with things that aren't normal. Maths has come with fuckall ways to deal with stuff like this.
Well you may say, this is absurd... There is nothing in reality that behaves this way. Well yes and no. You know how the building blocks of our universe obey quantum mechanics? The equations contain lots of infinities but only at intermediate steps. You have to "renormalise" them to make them go away. Nature apparently has infinities but likes to hide the from us.
The infinity problem is so fucked up. You know the reason physics people are unable to quantize gravity? Surely they can do the same thing to gravity as they did to say electromagnetic force? NOPE. Gravitation doesn't normalise. You get left with infinities in your final answer.
Anyways. Keep on learning, the world has a lot of information and it's amazing. And the only thing that makes us human is the ability to learn and grow from it. I wish you all the very best.
When Hilbert runs the hotel, sure, ok. Once he sells the whole thing to an ultrafinitist however you suddenly notice that there's a factory there and all the rooms are on rails and infinity means "we have a method to construct arbitrarily more rooms", but they don't exist before a guest arrives to occupy them.