But as long as we can define a number that is tangeble, it is subtractable from 1. It may take millions of miles of paper to write 3,000,000,000,000,000 9's, but there is still a value that can be obtained by subtacting that from 1.
But as long as we can define a number that is tangeble, it is subtractable from 1. It may take millions of miles of paper to write 3,000,000,000,000,000 9's, but there is still a value that can be obtained by subtacting that from 1.
Then that's the number.Originally Posted by Moo Moo the Ner Cow
I just didn't know of any way to write it. Maybe they actually do have some kind of symbol out there, and we just don't know about it.
And the easiest way to prove that 0.999... != 1 is to look at it this way:
Equal = The same as.
0.999... = infinite.
1 = finite.
finite != infinite
So maybe it can be bigger, maybe it can be smaller, but it's impossible for it to be equal to. And as any number less than one begins with "0.", you can't say that it is greater than 1. So therefore it is less than 1. Although anyone with a sensible brain knows that. Trying to get around it is useless... although pretty fun. It's similar to this theory I once read that 1 = 2. I can't remember for the life of me how it goes, but it was really confusing and stuff, much like this theory is.
Bow before the mighty Javoo!
And if .999... and 1 are equal to each other, give me a number, other than 1, that when subtracted from 1, will result in an answer of 0.
It's silly to find the digits of a repeating irrational number. Now, finding the digits of pi, that's different (don't ask me why)
And your 'smallest number less than one' is still easily written as 1 - lim (1/x) x->∞. Why write 0.11111111111111111111111111111111111111111111111111111111111111111111111111111... when you can write 1/9?
'smallest number less than 1'?
When did I say that?
EDIT: Also, I can see where 1 - .999... = .000...1, and as you never get to the 1 in .000...1, 1 and .999... are the same.
Good stuff. Yeah, math is fun.
Last edited by Flying Mullet; 05-10-2004 at 08:57 PM.
[q]But as long as we can define a number that is tangeble, it is subtractable from 1. It may take millions of miles of paper to write 3,000,000,000,000,000 9's, but there is still a value that can be obtained by subtacting that from 1.[/q]
The smallest 'tangible' number subtractable from one, when subtracted from one, is the largest number less than one. (forgiveness pls. I err....thought to say 'number with the smallest difference in value to one, which is less than one)
and it would be 0.999999999999999999999999999999999999999999... according to some sort of primitive way of writing math. Instead I prefer 1 - lim (1/x) x->∞.
No, no. Everyone who is not Unne or myself are wrong.
First off, repeating decimals ARE rational, because they can be converted into a fraction.
.222... is 2/9, and .999... is 9/9, or 1.
On that note, pi is irrational, because it cannot be made into a fraction.
Now, .999 with ANY number of 9s after it is less than 1. Yes, it approaches 1, but doesn't reach it.
"But as long as we can define a number that is tangeble, it is subtractable from 1. It may take millions of miles of paper to write 3,000,000,000,000,000 9's, but there is still a value that can be obtained by subtacting that from 1."
And that number is less than .999...
But infinity is not a number. The limit approaches inifinity, see? And when you REACH an infinite number of 9s after the decimal point, you get 1.
Ahh, okay. I was looking at it as a quote.
Anyway, I am curious to see if any knows:
if .999... and 1 are equal to each other, give me a number, other than 1, that when subtracted from 1, will result in an answer of 0.
It just sounds like an interesting proof.
I hate math again :(
Damn you Doomy I am still right about '2nd smallest number' :aimmad:
No, .999... is 999.../1000..., where the 9's and 0's are always the same amount.
Did you fail gr 10 math?
0.027 = 27/999
0.1 = 1/9
therefore
0.9 = 9/9 = 1
I think I was mistaken about the 'irrational number' because I thought that any number with no end of digits is irrational. If that's not the case, then what's irrational? A bunch of digits with no end, where the numbers don't repeat? I also thought a number expressible as a fraction is a radical.
:D
Yes you canYour 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.
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 nonsenseI 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.
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 nameI'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.
All pairs of numbers have a number in between, yes. Except when both numbers in the pair are identical.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.
You're straying from the topic hereOf 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.
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.0.999... + 0.999... = 1.999...98
I showed you in my first post how they're the sameI 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.
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
Dammit, I can't believe how complicated many of you can make simple and OBVIOUS thing like this to look like!
('-'*)/ - "sup"
Irrational numbers are numbers that cannot be expressed as fractions.Did you fail gr 10 math?
0.027 = 27/999
0.1 = 1/9
therefore
0.9 = 9/9 = 1
I think I was mistaken about the 'irrational number' because I thought that any number with no end of digits is irrational. If that's not the case, then what's irrational? A bunch of digits with no end, where the numbers don't repeat? I also thought a number expressible as a fraction is a radical.
PG - if you mean there is no second smallest number, you're right
"No, .999... is 999.../1000..., where the 9's and 0's are always the same amount."
infinity is not an amount
"what's irrational? A bunch of digits with no end, where the numbers don't repeat? I also thought a number expressible as a fraction is a radical."
Irrational numbers cannot be written as whole numbers or as fractions. My mind is blanking on what exactly a radical is, but it has something to do with roots.
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