/sci/ - Common sense argument as to why 0.9999... = 1

Name: Anonymous 2009-02-12 2:44

If you want to run a distance of 1 meter then you must first run 90% of the distance, and then 90% of the remaining distance, and then 90% of the remaining distance again, ad infinitum.

i.e. the distance in meters you must run is 0.9 + 0.09 + 0.009 + ...
which sums to 0.999...

So unless the sum adds up to 1 it's impossible to run 1m, which is nonsense.

Hence 0.999... = 1.

Name: Anonymous 2009-02-12 9:36

Don't even bother, man.

Name: Anonymous 2009-02-12 9:48

If you want to run a distance of 1 meter then you must first run 80% of the distance, and then 80% of the remaining distance, and then 80% of the remaining distance again, ad infinitum.

i.e. the distance in meters you must run is 0.8 + 0.08 + 0.008 + ...
which sums to 0.888...

So unless the sum adds up to 1 it's impossible to run 1m, which is nonsense.

Hence 0.888... = 1.

Name: Anonymous 2009-02-12 10:19

>>3
80% of the remaining distance is not 0.08.

Name: Anonymous 2009-02-12 10:33

Not this shit again.

Name: Anonymous 2009-02-12 12:03

>>1

Wow you're an even bigger faggot than AnOnYmOuS2U

Name: Anonymous 2009-02-12 14:31

At least trolls on /sci/ have some class..

Name: Anonymous 2009-02-12 14:45

>>4
Really?
shit, I guess it was a terrible argument then. Almost like I was trolling

Name: Anonymous 2009-02-12 15:25

CIRCLES ARNT REAL

Name: Anonymous 2009-02-12 17:28

>>8
Yeah, it couldn't possibly be that you're just a retard.

Name: Anonymous 2009-02-12 23:45

\lim_{n \to \infty}\left(\frac{9}{10} + \frac{9}{10^{2}} + \cdots + \frac{9}{10^{n}}\right) = \frac{\frac{9}{10}}{1 - \frac{1}{10}} = 1

Name: Anonymous 2009-02-12 23:47

[\lim_{n \to \infty}\left(\frac{9}{10} + \frac{9}{10^{2}} + \cdots + \frac{9}{10^{n}}\right) = \frac{\frac{9}{10}}{1 - \frac{1}{10}} = 1
\]

Name: Anonymous 2009-02-13 5:03

I step more than a meter every step. I guess that means I get there before I left.

Name: Anonymous 2009-02-13 10:37

>>10

Probably not lol, doing a maths degree

Name: Anonymous 2009-02-13 16:24

\lim

Name: Anonymous 2012-05-06 18:36

0.8+0.16+0.032.... = 1 = 0.9+0.09...

Common sense argument as to why 0.9999... = 1

1 Name: Anonymous 2009-02-12 2:44

2 Name: Anonymous 2009-02-12 9:36

3 Name: Anonymous 2009-02-12 9:48

4 Name: Anonymous 2009-02-12 10:19

5 Name: Anonymous 2009-02-12 10:33

6 Name: Anonymous 2009-02-12 12:03

7 Name: Anonymous 2009-02-12 14:31

8 Name: Anonymous 2009-02-12 14:45

9 Name: Anonymous 2009-02-12 15:25

10 Name: Anonymous 2009-02-12 17:28

11 Name: Anonymous 2009-02-12 23:45

12 Name: Anonymous 2009-02-12 23:47

14 Name: Anonymous 2009-02-13 5:03

15 Name: Anonymous 2009-02-13 10:37

16 Name: Anonymous 2009-02-13 16:24

17 Name: Anonymous 2012-05-06 18:36