You are not logged in.
Anthony, your concept of decimal expansion is way off. It has nothing to do with "making something bigger". 0.999... is not smaller than 1. Real numbers are static, they don't grow or change.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
to be honest, i think the proof:
is good enough without going into all this other math thats been mentioned.
Last edited by luca-deltodesco (2006-11-27 04:49:13)
The Beginning Of All Things To End.
The End Of All Things To Come.
Offline
To luca-deltodesco
I am sorry but you cannot multiply an Infinite by 10 or change an Infinite Number!
Offline
put it this way
means in laymans terms, a 0. followed by an infinite number of 9's, so if you multiply this number by 10, you shift the decimal point one place to the right, and you get 9, followed by an infinite number of 9's, if you then take away the first number, every single 9 after the decimal point in the second number, is cancelled out by the 9's after the decimal point in the first number, and you're left with 9.Last edited by luca-deltodesco (2006-11-28 03:40:19)
The Beginning Of All Things To End.
The End Of All Things To Come.
Offline
To luca-deltodesco!
The problem is it's impossible to know how many 9's there are in total!! because it's an Infinite Number! ie No End!.............................................................................................................
Offline
how is that a problem?
The Beginning Of All Things To End.
The End Of All Things To Come.
Offline
Anthony wrote:
The problem is it's impossible to know how many 9's there are in total!!
Then wrote:
because it's an Infinite Number!
That is the number of 9's. Non-finite.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
I just use:
When asked a question like this.
It's arguable, so I'm not saying that it's the absolute certain proof.
Offline
tbh, i dont understand how anyone can argue this simple proof? you get people saying, oh but when you times it by 10, there must be on less 9 on the end of it, but that doesnt make sense, because thats treating infinity as a definate value.
The Beginning Of All Things To End.
The End Of All Things To Come.
Offline
luca, the proof makes assumptions about binary operations performed on the decimal expansion of real numbers. Those assumptions turn out to be correct based on most standard definitions, but they are presented as assumptions none the less.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
If all Infinite Numbers equalled an Integer Number as in Infinite 0.9 = 1 it would be much easier to just call them Integer Numbers!!
Offline
0.999... is an integer!
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
To Ricky!
But how can any Number become! or is an Integer Number if it starts as . < 1
Offline
But how can any Number become! or is an Integer Number if it starts as . < 1
But that statement isn't true. There is a theorem which says:
In other words, if I have two numbers:
0.375.... (note that ... here means I know there are other digits, but I don't know what they are)
and
0.376.... (same thing here)
Without knowing any other digits, I can state that 0.375... <= 0.376 but I can not state that 0.375... < 0.376...
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
To Ricky!
Its Quite simple! I can also state that any number that has a . at the start! before the second part of the number! will always be smaller than 1
as in Infinite .9 will always be smaller than 1
Offline
Its Quite simple! I can also state that any number that has a . at the start! before the second part of the number! will always be smaller than 1
Sure, you can state that. But you'd be wrong. I've tried to explain how in as many ways as possible. (At least) Three different proofs have been in these threads show that 0.999... = 1, and you have yet to level one criticism against any of them. You just keep stating that 0.999... does not equal 1. Frankly, I feel like I'm talking to a brick wall, and I'm getting tired of it.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
Offline
To Ricky!
QUOTE: "I feel like I'm talking to a brick wall, and I'm getting tired of it."
This is a good point! at the end? of the Universe! and at the end? of an Infinite Number! there is a BRICK WALL! but unfortunatly behind the BRICK WALL! is an endless stream of .9's
Offline
This thread is a brick wall.
Offline
I'm a brick wall.
Offline
i completely agree with ricky
The Beginning Of All Things To End.
The End Of All Things To Come.
Offline
Genius! is seen in the eyes of others! when the problem is made clear! by the Genius!
A.R.B
Offline
Anthony - how about you start to prove the proofs false instead of writing nonsense
Support MathsIsFun.com by clicking on the banners.
What music do I listen to? Clicky click
Offline
I know this has probably been said before but:
and so by the same steps:
(did I make any mistakes in the proof?)
Last edited by Ehiness (2006-12-05 05:51:27)
Offline
OK LET'S SEE IF SOMEONE CAN REALLY PROVE THIS QUESTION!
Infinite 0.9 (stage one) the start! = 0.9 that is a 0 then a . then a 9 (this is the first .9)
If anyone can? using time a guide to how far the calculations have run,prove that Infinite 0.9 = 1 ?
0.9999999999999999999999999999999......
Ok! for every .9 above I am going to use (1) second of time!
So now give me! using time how long it will take for Infinte 0.9 to = 1
Example below!
0.9 = (1 second) 0.99 = (2 seconds) 0.999 = (3 seconds) etc.........................
Offline
That doesn't even make sense... Why would you do that? You can't keep on counting and eventually reach infinity. It's not a point, like the wall you described.
Support MathsIsFun.com by clicking on the banners.
What music do I listen to? Clicky click
Offline