Anything below 1 is lower than 1. I don't really see the problem.(.999... < 1)
Anything below 1 is lower than 1. I don't really see the problem.(.999... < 1)
If .999... is less than 1, then there's a number between .999... and 1. What number is between them? 0.00...1 isn't anything that makes sense. "A decimal, followed by 0's that never end; and once they end, put a 1 after the last one". No such thing.
Super, just super.
Now I just have to remember this crap for the fall. @_@
I am terrible at math so math makes me a sad person.
Algebra fine let me at it I can work that stuff baby its just all about the X = Y to the power of the Z ok that I can suffer it's kinda like making love to a girl you really hate but she's got the best body on the planet so you'll suffer just so you can say afterwards "See I did that babe there" and watch your mates drop in awe. However other than that get it the hell away from me
Prove it.Originally Posted by Dr Unne
Bow before the mighty Javoo!
In .000...1, the 1 comes AFTER the 0's.
Suppose the series of 0's is infinite. Then you can't put a 1 after it. If something is never-ending, you can't have anything after the end of it; it has no end. Infinity is not a number; infinity means never-ending. You can invent a number system where infinity is a number, or where there is a "greatest possible integer", but that number system is not our number system. Do you need a proof that there is no greatest integer in our number system? Suppose n is the greatest possible integer; I give you n+1; therefore n is not the greatest possible integer; this is a contradiction, therefore there is no greatest possible integer.
Suppose you CAN put a 1 after the series of 0's. Then by definition, the series of 0's is finite, because it has an end. If the series of 0's is finite, then it isn't between .999... and 1, no matter how many 0's you have. Suppose you have .0001. Well .0001 + .99999 = 1.00009. No matter how many 0's you have, I can have that many 9's plus one more 9 at the end, and then the sum will be greater than 1.
I get it... I think.
I detest math. The arts are for me.
If you can't have 0.000....1, then you can't have 0.999...Suppose the series of 0's is infinite. Then you can't put a 1 after it. If something is never-ending, you can't have anything after the end of it; it has no end. Infinity is not a number; infinity means never-ending. You can invent a number system where infinity is a number, or where there is a "greatest possible integer", but that number system is not our number system. Do you need a proof that there is no greatest integer in our number system? Suppose n is the greatest possible integer; I give you n+1; therefore n is not the greatest possible integer; this is a contradiction, therefore there is no greatest possible integer.
Suppose you CAN put a 1 after the series of 0's. Then by definition, the series of 0's is finite, because it has an end. If the series of 0's is finite, then it isn't between .999... and 1, no matter how many 0's you have. Suppose you have .0001. Well .0001 + .99999 = 1.00009. No matter how many 0's you have, I can have that many 9's plus one more 9 at the end, and then the sum will be greater than 1.
Your number is just as irrational and infinite as mine is. I can simplify my number by calling it "the second smallest number possible." Or, if I like
1 - 0.999... = x
You're only going by the theory of a computer. It's just a matter of "the next number above zero" - it's a number, sure. It's just impossible to say what it is. Use your imagination... it's a number beyond comprehension. 0.999... is just the same. How many 9's are there? An infinite amount. How many zeros are there? An infinite amount. You just need to think outside the square, so to speak.
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. 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. 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.
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.
EDIT: Just to play around even more with numbers.
0.9 + 0.9 = 1.8
0.99 + 0.99 = 1.98
0.999 + 0.999 = 1.998
0.999... + 0.999... = 1.999...98
I love it when logic is overtaken by imagination. The possibilities become endless.
Bow before the mighty Javoo!
maths makes my head hurt- but each to their own!
.999 = A screwed up decimal system?
hi BoB
the 'second smallest number' is simply the lim (1/x) x->∞
The idea is odd. There is no number between lim (1/x) x->∞ , or that the number is infinitely small.
Bingo.
Bow before the mighty Javoo!
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.
infinitely small does not mean 0.00000...1 or whatever it is you are thinking. It's smaller than that, but greater than 0.
In fact the 'number' is still lim (1/x) x->∞
[q]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.[/q]
No. You're thinking of 9/n + 9/n² + 9/n³ + 9/nx + 9/nx+1 + ... for { x | x є Z } ; that's a finite series, not the irrational number 0.999... ; finite series != 1. Infinite series = 1.
[q]Loony BoB's stuff[/q]
the 1 = 2 proof required some funny factoring that is wrong, if I'm not mistaken.
Your point about 0.999...being irrational (infinite) and 1 being rational (finite) is wrong because 0.999... is not irrational (it's 1!)
xD
Last edited by Peegee; 05-11-2004 at 09:10 PM.
Posting Permissions
