Thread: Does 0.9 repeated = 1?

Maybe, but It seems that 3 * 1/3 is close to 9/9 but not close enough to be exactly the same

What do you mean? 9/9=3/3=3*1/3

Originally Posted by pixies

Maybe, but It seems that 3 * 1/3 is close to 9/9 but not close enough to be exactly the same

This guy is either too young to be here, or he's a dropout.

I went to a uni interview on Wednesday and we talked about some interesting stuff... like how there's the same number of fractions as whole numbers (infinity). But more irrationals (a bigger infinity).

I think .9 repeated does and doesn't equal 1. It really depends on which reasoning you look at it from.

Oh ya
In b4 lock.

From a stand-point that defies all accepted mathematical fact and with reasoning that refuses to pay attention to calculus, yes, I suppose that's right.

Originally Posted by Xei

I went to a uni interview on Wednesday and we talked about some interesting stuff... like how there's the same number of fractions as whole numbers (infinity). But more irrationals (a bigger infinity).

It's called countable infinity and uncountable infinity. A set is countable if you can establish a one-to-one correspondence with the naturals.

I know.

So, basically, there is an infinite gradient between numbers and an infinite amount numbers can reach.

Uh.

Originally Posted by spockman

From a stand-point that defies all accepted mathematical fact and with reasoning that refuses to pay attention to calculus, yes, I suppose that's right.

It could be argued that not even .3 repeated can properly quantify 1/3. Hence the reason why .3 is repeated endlessly, because it can never reach a number close enough to actually be 1/3 of 1.

Since it is accepted in mathematics that .3 repeated does equal 1/3, then yes, .9 repeated does equal 1.

.9 repeated being equal to 1 makes things a whole lot easier.

Originally Posted by Kushna Mufeed

So, basically, there is an infinite gradient between numbers and an infinite amount numbers can reach.

No, because infinity is not a destination...it's a journey. An endless journey.

Lol, this debate is funny.

.3 isn't 'repeated endlessly' as if it's some kind of process. There exist an infinity of 3s in .3~. If there were a finite number it would be less than 1/3. As there are infinity, it is equal to 1/3.

0.333~ * 10 = 3.33~
3.33~ -0.333~ = 3
0.333~ * 10 -0.333~ = 3
0.333~ * 9 = 3
0.333~ * 3 = 1
0.333~ = 1/3

Originally Posted by Black_Eagle

It could be argued that not even .3 repeated can properly quantify 1/3. Hence the reason why .3 is repeated endlessly, because it can never reach a number close enough to actually be 1/3 of 1.

Since it is accepted in mathematics that .3 repeated does equal 1/3, then yes, .9 repeated does equal 1.

.9 repeated being equal to 1 makes things a whole lot easier.



No, because infinity is not a destination...it's a journey. An endless journey.

Lol, this debate is funny.

Only if you factor in time.

Time??

Saying that infinity is an endless journey implies it is a process which requires time. Infinity is independant of time.

Indeed. Mathematics is independent of time. Certainly number theory.

Let's not get into differential equations...

Originally Posted by Black_Eagle

It could be argued that not even .3 repeated can properly quantify 1/3. Hence the reason why .3 is repeated endlessly, because it can never reach a number close enough to actually be 1/3 of 1.

Took the worlds out of my mouth I thought about posting something similar.

1 can never be cut into 1/3.

And time cannot change that fact.

The derivative of infinity with respect to time?

Originally Posted by LucidDreamGod

Took the worlds out of my mouth I thought about posting something similar.

1 can never be cut into 1/3.

Uh...yes it can. And you just did it.

Originally Posted by Kushna Mufeed

The derivative of infinity with respect to time?



Uh...yes it can. And you just did it.

How did I just do it

.33333....
.33333....
+.33333....
.99999...

1/3

See? I did it again! I divided 1 into exactly 1/3!

______________
3|1.000000000...

Do it.

Am I the only one who gets the feeling that this thread is a debate between college students who have taken advanced math courses and freshmen in highschool?

Nope. :l

Originally Posted by Kushna Mufeed

1/3

See? I did it again! I divided 1 into exactly 1/3!

Looking at the title I thought you were talking about numbers represented with decimals, and not fractions.

I'm pointing out that the title question is, it will never get to 1.

However I did go into a bit of a problem with 1/3 is not in existence, it is, it just cannot be represented as a decimal, that is what I was meaning to say.

I was also saying that 1/3 is not equal to .3 repeating at least not perfectly. The current decimal system cannot represent that number.