lets see....

Damned mathematicians thinking there is a diffrence, us engineers know it doesn't matter.

[quote name='psyclo' date='Sep 17 2005, 01:43 PM']Damned mathematicians thinking there is a diffrence, us engineers know it doesn't matter.


[/quote]

mathmaticians know theyre the same.



lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1

0.9999... = 1



Thus x = 0.9999...

10x = 9.9999...

10x - x = 9.9999... - 0.9999...

9x = 9

x = 1.

You're implying that 10x has an extra figure, 10x - x should really be 8.999999....1



Mark

WTF that's just sad. Next time I'm going straight to bed when I get home.



Mark

thats only as it approaches infinity. It never truly gets to inifinity its just an approximation.

http://mathforum.org/dr.math/faq/faq.0.9999.html



and also:



http://www.straightdope.com/columns/030711.html

[quote name='7lufnis' date='Sep 17 2005, 03:43 PM']thats only as it approaches infinity. It never truly gets to inifinity its just an approximation.


[/quote]

its not constantly approaching it. its a set value.

Allright one last time.



in math we usually use base ten



hence 121 is read as 1*10^2 + 2*10^1 + 1*10^0 = 100+20+1 = 121



and 0.1 = 1*10^(-1)



However 10 is a somewhat arbitrary decision. Some ancient people did math in base 6. For my example we will use base 3.



121 in base 3 is 1*3^2 + 2*3^1 + 1*3^0 = 9+6+1 (base 10) = 16 base 10





Now consider 1/2 in base 10 this is written as 0.5. It has a definite value. In base 3 however it is written as 0.111~ because it cannot be represented with finite digits. The value is still exactly 1/2 not approaching 1/2 but exactly 1/2 but is symbolized by 0.111~.



Similarily in base 10 1/3 is written 0.333~. This is exacltly 1 part of 3 however one cannot write it in finite decimal expansion in base 10. In base 3 however the same number is 0.1



Finally 0.9~ is just one way of representing 1 in base 10. It's value is well defined like 1/2 is 0.11~ in base 3 is well defined. We do not do a function on 0.9~ nor is it rounded or an approximation. It is simply a valid representation of 1 in base 10



By the same argument 0.2222~ = 1 in base 3.

It means there's a squigly and you should have a margarita.