Quote Originally Posted by Loony BoB
If you can't have 0.000....1, then you can't have 0.999...
Yes you can Your 0.000....1 doesn't work because of your contradiction of sticking something after the end of something with no end - the 0.999... has no contradiction in it's meaning.


I can't see any proof against what I said earlier in what you just said. You're just using definitions. I don't care about definitions.
If you don't define anything, you can't really prove anything either since you'll have no rules to follow for a proof and can change meanings of everything to what you feel like, which, quite literally, is nonsense


I'm saying that there would be an irrational number between 1 and 0.999.... - it exists, it's just like Pi - you can't write it. It's impossible. So they give it a symbol instead! If nobody ever gave Pi the name of "Pi" and the little symbol, pi would not exist. But we all know it exists, it's just irrational. So give 1 - 0.999... (or, as I prefer to say, 0.000...01) a name. A symbol. And it will then exist.
No, there would only be a number in between 1 and 0.999... if 1 and 0.999... were different numbers. Since they're the same, as shown earlier, it doesn't exist, and you saying "it exists" on its own doesn't prove anything. Pi has nothing to do with anything here, you've just plucked a particular irrational number out of the air that happens to have a name. Since there's infinitely many irrational numbers, I should hope not every single one has a name They still all exist nameless though, giving a number a name doesn't magically bring it into logical existance.


People shouldn't be so narrow minded so as to say that there is nothing inbetween one number and the next - all rational numbers have an infinite amount of numbers between them. All irratoinal numbers have other irrational numbers inbetween them.
All pairs of numbers have a number in between, yes. Except when both numbers in the pair are identical.


Of course, neither of us can really prove the other wrong. It's just like a hyperbole, really. When you continuously half a number, and half it again, and so forth... do you ever end up with zero? Of course not. You just have a new half. That, too, will go on for infinity. There are so many irrational and infinite numbers that nobody can really comprehend it without naming irrational numbers and limiting infinite numbers.
You're straying from the topic here


0.999... + 0.999... = 1.999...98
Actually, you'll find the answer turns out to be 1.999... if you did it long hand. Again, you're contradicting yourself by putting something at the end of something with no end.


I don't see how no number between .999... and 1 proves that they are the same number. .999... will always be less than 1. You don't need multiple numbers in between two numbers to prove that they are greater than or less than each other. .999... will always be a fraction less than 1, no matter how small that fraction may be, thus .999... < 1.
I showed you in my first post how they're the same They're just different ways of writing 1. Would you say 65/65 < 234/234?


For everyone saying 0.999... is smaller than 1, prove it to me, instead of saying over and over that it just is without any backing Just because it looks smaller at a glance isn't sufficient, much like how many people mistakingly think square rooting a number will always lead to a smaller number, which doesn't work for numbers between 0 and 1.