Poll on math topic for school project

[chickenguy]

Pleas Answer the POll and don't close the thread as my project is due very very soon

 

[cepheid]

Fine. I voted "this is pointless" because you are trying to take a vote on something that is either true or false, and it happens to be TRUE. There is no doubt or controversy about it, so it doesn't make a very good project topic. I'm sorry to say it, but you should be looking into something else.

 

[t!m]

... unless the project is making a point of how unknown this TRUE fact is. Because personally I think it's rather interesting how many people would deny that .999... = 1. My only argument would be that to poll people from the Physics Forums, especially in the General Math section, is a bit innacurate as the voters are obviously more informed on the subject than the average person.

 

[Integral]

I few years ago there was a similar poll on Anatech forums. The result of over a 1000 votes was split about 60 - 40 with 40% getting it right.

 

[chickenguy]

Could anyone please put in any proofs to this thread and could you please explain this?

One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:

Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)

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

= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)

= .9/(9/10)

= 1