If you want a headache at 12am

[lefteyewilly]

click here and try to read

http://qntm.org/pointnine

not for you math geniuses, you'll just laugh and point at me

[yasunobu13]

not for you math geniuses, you'll just laugh and point at me

Haha, I was doing that in junior high.

The simplest explanation (but not a rigorous proof) for me was

0.11111... = 1/9
0.22222... = 2/9
0.33333... = 3/9
0.44444... = 4/9
0.55555... = 5/9
0.66666... = 6/9
0.77777... = 7/9
0.88888... = 8/9
0.99999... = 9/9 = 1.0

[sk8Krog]

Ok, cool and all, but he didn't take it as far as I thought he would.

Does that mean that then 0.7777... = 0.8888... since nothing can come between them?

[argonauta]

i think this quote says it all:
'Today, a young man on acid realized that all matter is merely energy condensed to a slow vibration - that we are all One Consciousness, experiencing itself subjectively. There's no such thing as death, life is only a dream and we're the imagination of ourselves. Here's Tom with the weather....' - Bill Hicks

[Ask The Geezer]

Sorry. I never got to the text. I saw his fractal in the header and got lost.

Good thing, cause I don't need a headache right now.

[luvenny]

Ok, cool and all, but he didn't take it as far as I thought he would.

Does that mean that then 0.7777... = 0.8888... since nothing can come between them?

0.7888...

[MechaPiano]

Does that mean that then 0.7777... = 0.8888... since nothing can come between them?

it only works with 0.999... and 1.000... this way, there are no middle number between 0.7999... and 0.800... though

and he is wrong! if there isn't a middle number than it only means that both numbers are sequent. you can't go from 0.999... to 1.000... without adding 0.000...001!

[luvenny]

I think yasunobu's explanation is the best

[MechaPiano]

I think yasunobu's explanation is the best

sorry, but 9/9 does not equals 0.99999...

[blazes816]

sorry, but 9/9 does not equals 0.99999...

0.99999... = 9/10

[MechaPiano]

0.99999... = 9/10

WHAT?! 9/10 = 0.9!

[wouter999]

That's a load of crock. 1.00000... - 0.99999... is not zero. It's an infinitely small decimal. Just because you can't write it out, doesn't mean it doesn't exist.

Also, his "real proof" is bull, because he seems to forget that when one limits a summation and calculates it, one also produces an estimate, in his case an infinitely small 0.1^n for n=infinite. Just because it is infinitely small, IT DOES NOT MEAN IT'S ZERO. In all his proofs he forgets that the concept of infinity leads to rounding and estimation.

[MechaPiano]

That's a load of crock. 1.00000... - 0.99999... is not zero. It's an infinitely small decimal. Just because you can't write it out, doesn't mean it doesn't exist.

Exacly! he just doesn't understand the meaning of infinity!
oh boy, let's just wait 'till he discovers i (-1^1/2)

[blazes816]

WHAT?! 9/10 = 0.9!

I was going on yasu's bases of how the numbers worked.

[MechaPiano]

I was going on yasu's bases of how the numbers worked.

oh...

[asun2art]

so when the gas prices say 9/10 it's actually 1 penny right?

[yasunobu13]

I was going on yasu's bases of how the numbers worked.

huh?

[gerbick]

this is quite wrong. dude doesn't even attempt to factor in things like asymptotes/limits where that recurring number of 0.999... will never truly ever reach 1.000... but it'll get damn close. Infinitely close.

He's looking for an integer/decimal number to be the "in-between" number when honestly it's going to be a formula that states that 0.999... != 1.000... due to it never ever reaching it. Simple addition/subtraction will continue to support his "claims", but every worthwhile equation that takes infinity and limits into place will prove him wrong.

[chris-sharpe999]

Gerbick did you read his bit at the bottom? 0.99... doesn't itself get closer to 1

Also, something that is infinately small IS zero. Eg take the sum of a geometric progression: Sn=a(1 - r^n)/(1-r) If you take this series to infinity you get S∞=a/(1-r) because the - r^n part becomes infinitely small, tending to 0.

"FACT: A sequence can only have one limit.

Observe that the limit of the sequence

0.9
0.99
0.999
0.9999
0.99999
...

is

0.9999...

That is, the sequence gets closer and closer to 0.9999..., in fact, infinitely close.

But the sequence also gets closer and closer to 1.0000..., in fact, infinitely close. So 1.0000... is a limit of this sequence too.

But a sequence can only have one limit, so 0.9999... and 1.0000... must be the same."

[gerbick]

gerbick did read it all.

0.9999 (repeating) approaches 1.0000 (repeating) but never gets there. That's a call a limit. No matter how infinitely close you get, you don't just quite there there.

It does get close... but not there.