# 0.9999.....to infinity is equal to 1

Discussion in 'General Chat' started by 996 911 Turbo, Jul 22, 2006.

1. The only way I can think of to halt the passage of time is to travel at the speed of light through space. And even then, it's only from the perspective of an arbitrary "stationary" observer. You could just as easily say that you are stationary and the observer is moving at the speed of light and it is he who experiences no time.

2. #352
Last edited by a moderator: Apr 25, 2016
We know it's at least larger than we can see. Doesn't mean we'll never have an answer, but the question is certainly far from being completely answered.

3. When you reach the end of the universe you start again at the other side.

4. There's a gorilla throwing barrels at you.

5. no. it's like the space everywhere growing.

6. according to Danger Mouse, it's just a white template.

7. #357
Last edited by a moderator: Apr 25, 2016
So if you just send a rock flying across the universe at the speed of light for bazillions of years, eventually it will hit a wall? A big, giant wall that surrounds the universe? I think not.

8. No, no one is claiming that. There isn't a wall at the edge of the universe, if the universe has an edge at all, which again, no one knows. For all we know it might enter another universe.

9. HOLY SHIT.

10. I was referring to the content of your post, not your spelling mistakes.

11. 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

= 9�0.1 + 9�0.01 + 9�0.001 + 9�0.0001 + ...

= 9�10-1 + 9�10-2 + 9�10-3 + 9�10-4 + ...

n=&#8734;
= &#931; 9�10-n
n=1

n=N
:= lim &#931; 9�10-n
N&#8594;&#8734; n=1

= lim ( 9�10-1 + 9�10-2 + ... + 9�10-N )
N&#8594;&#8734;

= lim ( 9�0.1 + 9�0.01 + ... + 9�0.000...0001 )
N&#8594;&#8734; \_______/
N-1 zeros

= lim ( 0.9 + 0.09 + ... + 0.000...0009 )
N&#8594;&#8734; \_______/
N-1 zeros

= lim ( 0.999...999 )
N&#8594;&#8734; \_______/
N nines

= lim ( 1 - 0.000...0001 )
N&#8594;&#8734; \_______/
N-1 zeros

= lim ( 1 - 10-N )
N&#8594;&#8734;

= lim 1 - lim 10-N
N&#8594;&#8734; N&#8594;&#8734;

= 1 - 0
= 1

this is a pretty good proof.

12. Copy/Pasting a proof including a lot of math most people won't understand doesn't make it a good proof.

13. yeah, that's not what makes it a good proof...

14. ha, yeah a good proof is something that proves something.

15. obviously I meant for this thread. Its pretty useless right now because a) its already been addressed and b) most of the people in this thread have trouble with the concept of limits, using a bunch of limits in a proof doesn't help them. Its obvious you're just trying to start stuff up again and bump your own thread.

16. 0.9999...... = 0.33333.... * 3
0.9999...... = 1/3 * 3

1/3 * 3 = 3/3
= 1

This has already been posted pages ago and I can't believe some people still don't accept it.