# Thread: What's wrong with this proof...

1. ## What's wrong with this proof...

Hello there. What's wrong with this proof:

1/3=0.3333333333...
3/1=3

(1/3)*(3/1)=(1*3/3*1)=(3/3)=1

and

(1/3)+(1/3)+(1/3)=0.3333333..+0.3333..+0.33333..=3*(1/3)=0.999999999999999

So 0.9999999999...=1

2. Originally Posted by jtl
Hello there. What's wrong with this proof:

1/3=0.3333333333...
3/1=3

(1/3)*(3/1)=(1*3/3*1)=(3/3)=1

and

(1/3)+(1/3)+(1/3)=0.3333333..+0.3333..+0.33333..=3*(1/3)=0.999999999999999

So 0.9999999999...=1
I really think you're allowed to round 0,9999999999999999999999999 off to 1.

3. Originally Posted by janvdl
I really think you're allowed to round 0,9999999999999999999999999 off to 1.
Yeah, but doesn't the proof above say 0.99999999999999999999... is equivalent to 1?

I'm a bit confused here.

4. Originally Posted by jtl
Yeah, but doesn't the proof above say 0.99999999999999999999... is equivalent to 1?

I'm a bit confused here.
No, most definitely not.

Look at this:

0,9 - close to 1
0,99 - even closer
0,999 - closer!

You get the idea.

See 1/3 = 0,3333333...
Those 3's never stop. They go on into infinity.

So what does that mean?
0,99999... is always tending to become 1. It will get so close to 1, that we could just as well right 1.

Do you understand?

5. Originally Posted by janvdl
No, most definitely not.

Look at this:

0,9 - close to 1
0,99 - even closer
0,999 - closer!

You get the idea.

See 1/3 = 0,3333333...
Those 3's never stop. They go on into infinity.

So what does that mean?
0,99999... is always tending to become 1. It will get so close to 1, that we could just as well right 1.

Do you understand?
So if the 3's in 0.3333.... never stop, then shouldn't it be infinity?

6. Originally Posted by jtl
So if the 3's in 0.3333.... never stop, then shouldn't it be infinity?
No.

The 3's only keep repeating. Infinity is different.

Don't try to make things harder. Keep it simple.

0,99999999 is always getting closer and closer to 1. It will later be so close that we could just as well write 1.

7. First of all thanks janvdl. And yes I know you can round it off. This isn't homework or anything to do with school. I just wrote that proof, and I'm wee bit bewildered.

My question is regarding the proof, whether it's wrong or not. That's what's confusing me.

8. Originally Posted by jtl
First of all thanks janvdl. And yes I know you can round it off.

My question is regarding the proof, whether it's wrong or not. That's what's confusing me.
Can you give me the actual question please?

I can see nothing wrong with using either 0,333... or $\frac{1}{3}$, its the same thing.

9. Originally Posted by janvdl
Can you give me the actual question please?
There's no question. That's the proof, i'm asking whether there is something wrong with it.

10. Originally Posted by jtl
I just wrote that proof, and I'm wee bit bewildered.
My question is regarding the proof, whether it's wrong or not. That's what's confusing me.

11. Originally Posted by jtl
There's no question. That's the proof, i'm asking whether there is something wrong with it.
No, as far as i know, there is nothing wrong with using either 0,3333... or $\frac{1}{3}$, because they are the same thing, so i would say no, there isn't anything wrong with the proof, not on my level or your level of mathematics anyway.

This can get kind of complicated, im thinking of hyperbolas. 0,9999... is always nearing to 1, but never actually becomes 1...

12. Originally Posted by Plato
I finished my A'Levels (basically highschool) and took a gap year before uni. My mathematical knowledge has been drained because of the gap year, I need to start learning again.

My level of knowledge on Geometric Series is well nothing cause I don't remember much.

Any ways, if this involves geometric series, it would be real helpful if you could give me some points or links to get this.

Thanks.

13. Originally Posted by jtl
I finished my A'Levels (basically highschool) and took a gap year before uni. My mathematical knowledge has been drained because of the gap year, I need to start learning again.

My level of knowledge on Geometric Series is well nothing cause I don't remember much.

Any ways, if this involves geometric series, it would be real helpful if you could give me some points or links to get this.

Thanks.
I am not sure how to apply this to a geometric series, so it would be better if Plato takes over from here.

14. Originally Posted by janvdl
I am not sure how to apply this to a geometric series, so it would be better if Plato takes over from here.
No problem. Thanks anyway.

Oh and plato, so is the proof wrong?

15. Originally Posted by jtl
Hello there. What's wrong with this proof:

1/3=0.3333333333...
3/1=3

(1/3)*(3/1)=(1*3/3*1)=(3/3)=1

and

(1/3)+(1/3)+(1/3)=0.3333333..+0.3333..+0.33333..=3*(1/3)=0.999999999999999

So 0.9999999999...=1
The result you "prove" is correct but you are using processes that you do
not justify. In particular how do you know that:

0.333..+0.333..+0.333..= 0.999..

what method have you used to add the things on the left of this
equation?

RonL

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