MATH questions

There is no dispute amongst mathematicians as to whether 0.999...=1 or not.  It does.  The wikipedia article on the subject is correct.

Incorrect again. I am a mathematician (possibly a very poor one) and I dispute it.

Ramanujan is a phenominal case:

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

On what basis?

Wow. Never seen that. Shame it has absolutely nothing to do with Euler or Reimann's proofs. So, yeah. :)

If two numbers are not the same, there are an infinite number of numbers between them.  For example, 0.99 is not the same a 1.  This can be proved because 0.995 is between 0.99 and 1.

But 0.999... (repeating infinitely) is equal to 1.  If they are not equal you should be able to find a number between the two.  You cannot.

Case closed 

There are 100s of boring Internet threads with people arguing over the topic.

Clearly we are working on different number system. Perhaps you're working on the real number system appended with an infinitesimal?

The limit argument isn't compelling to me; try to define a non-trivial series that actually reaches its limit.

This one from OnStar is more interesting.

0.999... is defined to be the limit of the sequence (0.9, 0.99, 0.999, ...), just like 0.333... is defined to be the limit of the sequence (0.3, 0.33, 0.333, ...). If you don't accept definitions, then you don't accept axioms and there's no use arguing because we're working on different axioms.

Disproof should be realatively straightforward, do you have a counterexample that meets OnStar's criteria?

Alternatively, 1 - 0.999... should give us a non-zero value if they are not equal.  What is this value?

steve_bute -

What exactly about open sets and their boundaries has anything to do with .999... =/= 1?

Is the thought that you couldn't evaluate (0, .999...) as an open set? I don't see any issues myself...

Also, let me just offer this up since it seems you have a better understanding of math. You say that .999... is not 1. You say this is true in the good old standard number system. However, the standard number system also has the quality of the denseness of Q. So I suppose you have to say that .999...<1. So feel free to tell me what rational number falls inbetween .999... and 1.

My concern about set boundaries lies with analytic functions. Knowing whether the set that a function operates on is open or closed is of great importance.

I'll admit a gap in my knowledge; I'll pursue it.

A good day, a good argument, thanks everyone.

This has nothing to do with Euler. TheGrobe has missed the "more advanced" proof for this, that avoids the "pitfalls" described in the article. Euler and Reimann proved this differently. Don't take the first thing you see to be the truth.

I didn't; I merely thanked him for posting the link. Don't take your first thought to be logical :).

Ha, well played. :)

I have simply explained that all so called "proofs" of 0.999..=1 already assume the result by using 0.000...01=0 at some point in the proof.

0.999..=1 is only true by definition.

While I know and agree that 0.999..=1, it irritates me when people proudly present these flawed proofs.

Infinite series vs. Infinite limit of a series.

Infinitesimals do not exist in the real number system. Using them to disprove something is just as bad as diving by 0 to prove something.