No, from my class, pretty much every time with these series it meant that these series APPROACHED these numbers.  However they never actually reached them.  In calculus you simplified them to such.  The formula is simply one that is used to handle more complex geometric series, such as ones that may approach a number like .253 or something.  

However, since the sum goes on infinitely, it does not ever actually equal to the number itself.  

Wouldn't it actually have to be repeating y and not repeating zero? I would consider it repeating zero but the actual quantity trying to be subtracted from one is not definitive.

I take it math isn't your strong subject?  That or you haven't taken higher levels of math.  The whole distinction for 0.35 and 0.350 and going on is mostly a distinction made for science.  They use it to keep their "significant figures" as they need to keep their measurements as accurate as they were able to measure, whatever they were measuring, with.

Top-10 university Physics degree with considerable maths content. It's just an example to show that two different decimal numbers equal the same number, which is usually the hurdle for not understanding this problem.

You can try to make "proofs" that .9 repeating = 1, but this only can work if you ignore the fact that our decimal system doesn't work perfectly.

They're not proofs that .9999=1, they're examples that show they both represent the same number.

Nothing in this thread so far is a rigorous proof, but that doesn't change the conclusion.

...

I said "proofs" as in math proofs.  Equations that show the work.  

Nothing in this thread is a math proof.

They are formulas of what people use as proofs for it.

However, .9 repeating only represents 1 as applied to the real world due to the fact that .9 repeating does not exist as a number.  

"Existing" doesn't come into it. It represents the same object as 1.

This is a rather vague statement that I would agree with if I knew what you meant by it.  The way the OP explains it I do not agree with.  

It's the same thing as not being able to use infinity as a number in your equation, because it isn't.

Infinities are treated very differently in pure maths. They can be used correctly if you know what you're doing.

.9 is an example of infinity because it is only able to be logically produced by one.  9/9 doesn't equal .9 repeating unless you assume that 1/3 is literally a compilation of 3's behind 3's, but the thing about 1/3 = .3 repeating as a decimal has to do with the fact that decimals represent 10ths.  If you used a different numerical system, 1/3 would not have to be a repeating number. .9 is different in that it would be repeating regardless.

 Also, if we say an object cannot get any bigger than a certain size and no smaller than a certain size, 1/3 will not actually equal .3 repeating infinitely.  It would go to a point where it actually ends.

You're still imagining real "things" which must have a finite extent. Something going on infinitely in that representation doesn't automatically disqualify it. I mean, with maths you can take apart a sphere and reassemble it into two spheres of equal size with no logical contradiction. It's physically impossible but perfectly correct.

Hmm, "must have finite extent" isn't exactly true as we do not know that yet.  But that's irrelevant anyway.  

However there's a reason 1/3 goes on infinitely on representation (as well as some of the others).  It has to do with the way we measure things to begin with.  They actually are finite measurements.  .9 repeating isn't for the reason that the reason it exists is because something is always being added to it to make it .9 repeating. 

If you want to make it into one, then yes make it represent 1. 

What are you trying to say by "this is a logical"? .9 is 1. You round it up. A number that is rounded up becomes that number therefor it was already one.