1 = .999..... Right?

Dr.Seussicide · 07-30-2010, 10:15 AM

Quote:

Originally Posted by noise

is this like a cross between "super silly" and "super serious"?

It's a word

But I meant to say superfluous.

swim · 07-30-2010, 04:05 PM

Quote:

Originally Posted by TheBig3KilledMyRainDog

I'm kinda turned on right now.

I'm flattered.

Dom · 07-30-2010, 05:00 PM

Quote:

Originally Posted by HereWeGo

sorry, but you are completely wrong.

.9999 repeated does not equal 1, but for each 9 you add it gets closer to 1.

Where's your proof? Wikipedia (amongst many other sources) would say otherwise.

thomasracer56 · 07-30-2010, 05:01 PM

This is EXACTLY what I had wondered about... I had put together everything but the conclusion, then I just dropped the subject.

noise · 07-31-2010, 12:45 PM

take a distance, A to B.
move 90% of that distance.
then 90% of the remaining distance.
and so on and so on, to infinity.
how will you ever get to B?

reminds me of zeno's dichotomy paradox...

swim · 07-31-2010, 12:50 PM

This isn't a matter of limits. It's matter of the rationalizing repeating decimals.

So let's look at 1/3 it divides out to .3 repeating.
These two quantities are equal.

so if we multiply both quantities by three we will 1 and .9 repeating.
These two quantities are equal

there's no discussion to be had

noise · 07-31-2010, 01:06 PM

.3 repeating is very close to 1/3, but even if you carry it out to the end of the universe, they're never actually equal, are they?

midnight rain · 07-31-2010, 02:09 PM

Quote:

Originally Posted by noise

.3 repeating is very close to 1/3, but even if you carry it out to the end of the universe, they're never actually equal, are they?

Um, yes, they are.

If 1/3 doesn't equal .3 repeating, then enlighten all us math noobs as to what the decimal equivalent of that fraction is...

swim · 08-01-2010, 09:44 AM

You seem to stuck on the concept of limits.

.3 repeating is a rational number so you can rewrite as a fraction if you wish and the are the same. It all goes back to geometric series really. And 3rd grade division.

cardboard adolescent · 08-02-2010, 01:18 AM

Quote:

Originally Posted by Seltzer

Look, I know it seems counter-intuitive to believe that 0.9 recurring = 1, but you have to trust me on this one

Your reasoning follows on from this:

2 - 1.9 = 0.1 = 10^-1 (which is more than 0)
2 - 1.99 = 0.01 = 10^-2 (ditto)
2 - 1.999 = 0.001 = 10^-3 (ditto)

General Form:
2 - 1.9{n} = 10^-n where 9 is repeated n times (which is more than 0)

That reasoning is fine for a finite n. But as n tends towards infinity, limit(10^-n) = 0. In other words, that 0.000...001 number you quoted is basically 1/∞ which is considered to be zero, meaning that 2 - 1.999... = 0 (which makes sense since 2 is 1.999...)

Wait... so if you take 1 and break it up into smaller and smaller pieces... it's ultimately MADE OF ZEROES?!?! HOLY SHIT!!! EVERYTHING IS NOTHING!!

... I guess that's why it's so easy to get from A to B. Ain't really goin' anywhere, are ya now?

07-31-2010, 12:45 PM	#35 (permalink)
noise thirsty ears Join Date: Sep 2009 Location: Boulder Posts: 742	take a distance, A to B. move 90% of that distance. then 90% of the remaining distance. and so on and so on, to infinity. how will you ever get to B? reminds me of zeno's dichotomy paradox... __________________ my flac collection

07-31-2010, 12:50 PM	#36 (permalink)
swim dontcareaboutyou Join Date: Apr 2006 Location: North Carolina Posts: 5,188	This isn't a matter of limits. It's matter of the rationalizing repeating decimals. So let's look at 1/3 it divides out to .3 repeating. These two quantities are equal. so if we multiply both quantities by three we will 1 and .9 repeating. These two quantities are equal there's no discussion to be had __________________ http://nakednaps.bandcamp.com/

07-31-2010, 01:06 PM	#37 (permalink)
noise thirsty ears Join Date: Sep 2009 Location: Boulder Posts: 742	.3 repeating is very close to 1/3, but even if you carry it out to the end of the universe, they're never actually equal, are they? __________________ my flac collection

08-01-2010, 09:44 AM	#39 (permalink)
swim dontcareaboutyou Join Date: Apr 2006 Location: North Carolina Posts: 5,188	You seem to stuck on the concept of limits. .3 repeating is a rational number so you can rewrite as a fraction if you wish and the are the same. It all goes back to geometric series really. And 3rd grade division. __________________ http://nakednaps.bandcamp.com/

07-30-2010, 05:01 PM	#34 (permalink)
thomasracer56 Still Crazy Nutso! Join Date: Oct 2009 Location: California, USA Posts: 148	This is EXACTLY what I had wondered about... I had put together everything but the conclusion, then I just dropped the subject.