# Just for fun

• Mar 4th 2010, 11:14 AM
helpwithassgn
Just for fun
I saw this somewhere but I can't remember the reason behind it.

1/3 + 1/3 + 1/3 = 1

1/3 = 0.333333333... recurring

but then

0.333333 + 0.333333 + 0.3333333 = 0.999999999...
• Mar 4th 2010, 09:48 PM
arcketer
Quote:

Originally Posted by helpwithassgn
I saw this somewhere but I can't remember the reason behind it.

1/3 + 1/3 + 1/3 = 1

1/3 = 0.333333333... recurring

but then

0.333333 + 0.333333 + 0.3333333 = 0.999999999...

Well, one can express 0.99999 (repeating) as the limit as x goes to infinity of the following:

The summation (Sigma sum indexed by i bounded from 0 to x) of 9 divided by 10 * 10^i.

If you compute that, you'll see that the limit goes to 1.

That's just one unneccessarily complex way to look at it.
• Apr 24th 2010, 10:11 AM
Chokfull
I like this problem-- $1-\frac {1} {\infty}=.99999999999....$

Therefore, one over infinity equals 0 if $\frac {1} {3}*3$ is to equal 1.

This shows that $\frac {1} {0}$ is infinity, also proven by $\tan 90^o$ being $\infty$, and also being the slope of a vertical line, or $\frac {1} {0}$
• Apr 24th 2010, 01:59 PM
Defunkt
Quote:

Originally Posted by Chokfull
I like this problem-- $1-\frac {1} {\infty}=.99999999999....$

Therefore, one over infinity equals 0 if $\frac {1} {3}*3$ is to equal 1.

This shows that $\frac {1} {0}$ is infinity, also proven by $\tan 90^o$ being $\infty$, and also being the slope of a vertical line, or $\frac {1} {0}$

$\frac{1}{0}$ is not infinity; it is not defined.

Usually, we say two numbers $x,y \in \mathbb{R}$ are different, if there exists $c \in \mathbb{R}, ~ c \neq 0$ such that $x-y=c$. In this case, what is $1-0.999...$? Is it non-zero?
• Apr 25th 2010, 10:03 AM
wonderboy1953
Comment
of course you know that $1/{\infty}$ is nonsense.
• Apr 25th 2010, 10:57 AM
Wilmer
Quote:

Originally Posted by wonderboy1953
of course you know that $1/{\infty}$ is nonsense.

Not really: was 1/8, but the 8 went to bed... (Giggle)
• Apr 28th 2010, 12:31 AM
Bacterius
Quote:

Originally Posted by helpwithassgn
I saw this somewhere but I can't remember the reason behind it.

1/3 + 1/3 + 1/3 = 1

1/3 = 0.333333333... recurring

but then

0.333333 + 0.333333 + 0.3333333 = 0.999999999...

The reason for this is that, theoretically, 1/3 + 1/3 + 1/3 is strictly equal to one, but in practice, as no-one can fully represent an infinitely recurring decimal, the sum of 1/3 + 1/3 + 1/3 will tend towards 1 but will never actually reach it. You can't manipulate recurring decimals algebraically without using fractions. Algebra just hasn't been designed for it.

This is one of the advantages of mathematics in my opinion : by defining some axioms and building everything upon it, it is possible to prove things without actually having to check whether it works : if the axioms remain the same throughout the proof, and the proof is valid, the experimental results will follow.