Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote -3 down vote favorite

Possible Duplicate:
Does .99999… = 1?

I was thinking about this the other day...

if 10/3 = 3.33333... (series)

why doesn't 3.333... * 3 = 10 it can never be 10 it's always almost 10 or 9.9999... (infinity)

I have read about this but then no one has an answer yet we all accept the fact that it is true when the statement is fundamentally false.

share|improve this question
6  
$10=9.9999999...$ – Amr Jan 24 at 21:21
3  
(Abstract) duplicate of Does .99999… = 1? – Zev Chonoles♦ Jan 24 at 21:22
3  
I smell a troll... – Mike Jan 24 at 21:34
1  
@Val either you are trolling or you arent comprehending what infinity is. Subtract 9.9999... from 10. What happens? Lets see. $10-9.9=0.1$, $10-9.99=0.01$,... $10-9.999...999=0.000....001$ to infinity $\Rightarrow 10-9.9999...=0.00...$. The 1 never appears! Therefore, $10-9.999...=0 \Rightarrow 10=9.999....$ – CBenni Jan 24 at 21:47
1  
@Val and Indeed, there are theories of mathematics (particularly hyperreal numbers) where 9.999... is INFINITESMALY smaller than 10. Which means, the difference is smaller than any real number. What we mean when we say $10=9.9999...$ is $St(10)=St(9.\overline{9})$ – CBenni Jan 24 at 21:50
show 8 more comments

marked as duplicate by Ross Millikan, 5PM, Ittay Weiss, Micah, Ayman Hourieh Jan 24 at 22:34

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

3 Answers

up vote 4 down vote

If $9.9999...$ and $10$ are not the same number, then name a number between them.

share|improve this answer
1  
Doesnt mean they are the same ;) (Of course it does, but that would have to be shown at least) – CBenni Jan 24 at 21:24
1  
But of course. But almost everybody knows two unequal numbers have a number strictly between them, and those that don't can be shown it fairly quickly using elementary inequalities. Better than trying to explain limits to someone who likely has a pre-calculus level. @CBenni – Thomas Andrews Jan 24 at 22:52
up vote 2 down vote

When we say that $\frac{10}{3} = 3.333\dots$

We have it like this:

$$ \text{Let } p = 3.3333\dots $$

$$10p = 33.33333 \dots$$ or

$$ 9p = 30 $$ or

$$ p = \frac{30}{9} = \frac{10}{3} $$ That's how I've always convinced myself of the proof. :|

share|improve this answer
I believe since we can't never have truly 0 (nothing), something must give way, e.g: 3.3333 * 3.00000=10 maybe because 0 may not mean absolutely 0 if that makes sense? there must be one point on the serious where something must give way? – Val Jan 24 at 21:32
up vote 0 down vote

$10/3=3.\overline{3}$

$3\cdot 3.\overline{3}=9.\overline{9}=9+\dfrac{9}{9}=10$

This should answer your question pretty much.

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.