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
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?
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.
Thanks again for your replies.
No, as far as i know, there is nothing wrong with using either 0,3333... or $\displaystyle \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...
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.