How does them existing in some other system imply the system is flawed? I can very well define 0.999..=0, which is true in the trivial ring, but this shouldn’t have any implications on the validity of the field of real numbers.
But between two different rational numbers there is infinte numbers so find me one. Let me give you an example between 2 and 4 there is 3There is nothing between them because the difference is the smallest infinitesimal possible.
Infinitesimal - Wikipedia
en.wikipedia.org
It doesn't work that way when the difference is the smallest it can possibly be.
1.333…2 is not a well-defined expression.
Because it creates a paradox. The product of two numbers cannot have multiple values unless one of the numbers also has multiple values.
I think my issue is saying that the limit of a number is the same as that number.
A number having multiple values is not well-defined, so I’m not sure what you mean. This doesn’t create a paradox, different statements are true in different fields. In the field of real numbers, 1=0.999…, and in the trivial field, 1=0. This isn’t a contradiction.
What happens if you split a quark in two? As far as we know, quarks are indivisible. Same with the smallest infinitesimal. I guess if you represented it as 1/infinity, you could say halving it is 0.5/infinity but that could also be considered the same as 5/infinity.
That is how an infinite decimal is defined. The limit of the finite portions of it.
Yeah it's pretty much this. The varied number of times we have had this issue where they immediately just jump to Tier 1/0 characters without any substance is just, a little gratting.
I hardly see how physics is relevant to math, but I assume you’re suggesting dividing an infinitesimal is not well-defined, which is very odd, as that is tantamount to saying multiplying two numbers isn’t always defined. Division by 2 is the same thing as multiplying by the multiplicative inverse of 2, 1/2. Whatever system your working with is a very strange system of “numbers” if it doesn’t satisfy any of the properties the real numbers do that are relevant, e.g. multiplication of any two real numbers is defined, and it’s Cauchy complete. Asking if 0.99..=1 is a question about two real numbers, not two elements of some arbitrary odd system.
Then the definition is an estimate.
What exactly are real numbers estimating?
I have no idea, at first everyone was just trying to give this dude some criticism and advice on how to make sure his manga is actually any good, and when I come back it’s a math debate
I don't see why we can't say 0.9... with Rayo's Number 9s trailing off isn't also 1. If that's not enough, we can do Graham's number.
The value of an infinite decimal.
But an infinite decimal is defined to be a real number. This is how it’s been defined since we’ve had foundations for real analysis. What would you suggest the entire mathematical community at large redefine the term “real number” to mean? A surreal number?
Thank you.
Not sure what you mean by that, do you mean with only finitely many 9’s?
I don't have issues with the definition of a real number. But it's not the only system it can be applied to. The surreal number line contains real numbers so it is relevant there.
I don't understand why it is less than 1 but another number that would logically be less than 1 isn't. Both would logically be less than 1. Why does mathematics say otherwise? In both cases, the difference might as well be zero in almost every situation.
I'm not sure about anyone else, but I'm not saying to not use your own tiering system. People do it all the time. I'm only saying it doesn't really have a point to debate this here of all places in a place where that discussion wasn't even the point of the initial OP as it's already been answered. If he wants to make his own personal tiering system, that's perfectly valid, it just wouldn't really work as an argument in any place with it's own tiering system, especially one with an absolute peak that is functionally intended to not be able to be surpassed (which a lot of people says spits in the face of Fiction which again I agree with but I don't mind if Tiering Systems have more restrictive tiers. It keeps things more grounded) .
I still have 5 pages to read somehow. But I just want to note that a lot of people including me are here for human and superhuman level power scaling. I am pretty much here entirely for lower tier versus threads.
But there is literally a proof that it does? Real numbers are a dense set which means that for ANY real number x and ANY posetive distance there is a set that contains x and another real number. Or in another words between any two real numbers there must be another real number.
I don't really have any human or superhuman OCs. I have an Undertale AU where everything is hypoversal (which isn't a tier on here but is on some other wikis) but every other main character or standalone OC I have is at least wall level.
The difference between them isn't 0. It's 0.00000000...1 with infinite zeroes.
What I am trying to say is people are going to be interested in different tiers. for me the best thing is some 9-C matchup, while other people enjoy 1-A matchups and seeing if the two characters can even interact with each other. If something is well written and interesting people will like it. Like me personally anything past tier 3 is entirely boring usually.
Correction:
It does fit that since all of them are smaller and weaker than string matter which is 1D.
So prove that it is a real number then
The difference is a very small, but still non-zero number in the first case. There is a huge difference between “really small” and “0”. Just because it’s really small doesn’t mean logic dictates it’s 0 or vice versa. The reason 0.999..99 n times is not 1 is because there’s a real number between the two.
It's a surreal number. It's not a real number. But the surreal number line contains all real numbers.
I don’t think they’re claiming it is one.
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