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Whether or not it seems that way is irrelevant. .999 repeating 'is' 1. In this context, infinitely close is congruent.Quote:
i've never even thought about this lol.... but I guess I would say they're not equal, since .999 will always be slightly less than 1, and .9999, and .99999 and forever on won't ever be 1.
Example: .3 repeating equals 1/3 right?
and .3 repeating times 3 equals .9 repeating, right?
and 1/3 times three equals one
Therefore one must equal .9 repeating
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
This guy is either too young to be here, or he's a dropout.Quote:
Originally Posted by pixies
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.
It's called countable infinity and uncountable infinity. A set is countable if you can establish a one-to-one correspondence with the naturals.Quote:
Originally Posted by Xei
I know.
So, basically, there is an infinite gradient between numbers and an infinite amount numbers can reach.
Uh.
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.Quote:
Originally Posted by spockman
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.Quote:
Originally Posted by Kushna Mufeed
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
Only if you factor in time.Quote:
Originally Posted by Black_Eagle
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... :P
Quote:
Originally Posted by Black_Eagle
Took the worlds out of my mouth :P 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?
Uh...yes it can. And you just did it.Quote:
Originally Posted by LucidDreamGod
How did I just do itQuote:
Originally Posted by Kushna Mufeed
.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
Looking at the title I thought you were talking about numbers represented with decimals, and not fractions.Quote:
Originally Posted by Kushna Mufeed
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.