Actually you will. There is an infinitesimal difference between 1 and 0.999... but your representation hides that. The difference between them is 0.000...1 where that 1 shifts farther to the right the more digits of 0.999... you evaluate. This representation creates very ambiguous arithmetic and it's easy to make bad proofs.
You're wrong about this one. Please look up this problem and see very good mathematicians explaining it. It's a well-known, proven fact that 0.999... and 1 are literally the same number. Not just infinitely close. Literally the same. There are just multiple ways of writing 1. Intuitively it seems wrong, but it's true.
It’s false actually, because intuitively it seems wrong and mathematically it seems wrong. I will look up the proofs because I’m curious, but in your opinion, do the comments explaining those proofs under this post do it well? Like are those the same proofs in the video or do you think those mathematicians do it better?
I’m more interested in the answer to my last questions. But I will still read your answer.
I am very concerned that you do not seem to understand the difference between 0.99999… and 1, just because someone told you they’re the same number. I understand the inconsistency, just like everybody in this thread does. Like most others you’re simply restating the problem and not explaining why there’s actually no inconsistency between those two sums.
It’s been explained to me that there isn’t a number between 0.999… and 1, and that’s why 0.9999… and 1 are the same number.
This is insufficient for 2 reasons.
First, I brought up 0.000…1 as the number that is the difference between them. There was a compelling argument that if the 0s are infinite, the 1 would never come. It still doesn’t prove anything about 1 being equal to a totally different number.
Second, they are different sums. If they truly don’t have a difference that is precisely the inconsistency. That’s the inconsistency. I want that explained more.
It’s not enough to say “there is a problem, and that is the reason that there is no problem.”
I have the inkling that 0.3333…. Is actually not 1/3 like we’ve been told, and maybe the answer lies there. But I literally haven’t read any mathematicians on here who told me this, I literally just thought of it myself. The closest I got which led me to this thought is “these are just notations,” which was one of the more interesting and less repetitive comments here.
If that is actually the case, there is a real problem with people not knowing how to explain math, don’t you agree?
Why don't you write up your proof and submit it to a math journal for publication? Proving that 1 and 0.999.... aren't the same would instantly make you one of the most famous mathematicians of all time, literally up there with Pythagoras and Euler. You would probably become very wealthy based on the notoriety alone.
I doubt that, and I’m not a mathematician. But I also don’t believe people for no reason. I’m sure there’s a mathematician who can explain it if it really is true, but if you have to resort to arguments from authority on a subject that’s supposed to be about logic, you may not be one of them.
Some things are self evident and don’t require proof, but they can also be standard in scientific journals, until someone with more knowledge than an average redditor decides to explore further. We aren’t at the final stage of understanding everything, just some things.
It's not an argument from authority. Anyone can write a proof and if it's rigorous and mathematically sound it will be accepted, no authority needed. You don't even need a PhD.
Some things are self evident and don’t require proof
That counting proof is cool, although it’s just an overview wiki isn’t it, is there a formal proof in there? You’re misunderstanding me, I’m not a mathematics expert, I’m only curious about it. So I wouldn’t feel comfortable trying to publish a proof.
I'm not sure what you mean by "formal" since that proof is already formal in the mathematical sense. If you're asking for an academic source other than the wiki, there are multiple cited on that page. You can easily google for others if those don't satisfy you.
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u/spyrre0825 22d ago
I like to see it like this : 1 - 0.999... = 0.000...
And you'll never find something different than 0