0.222... has an exact position in 2.222... and the same holds for 0.999... in 9.999... and generally any 0.###... (where # is the highest value of any base n>1) has an exact position in #.###...

My new representation method clearly shows that the initial 0.###... entity is definitely not the result of #.000*X/#.000 = 1, and all you do is to eliminate 0.###... by #.###... - 0.###... subtraction, and then you use #.000*X/#.000 = 1 in order to get your requested result, which is clearly not 0.###... entity (marked by purple in my argument), which was simply replaced by you by 1 (which is another entity, marked by green in my argument) in order to get the requested result, which is false if you insist that the initial X=0.###... and the result X=1 are the same mathematical entity.

What I have discovered in this argument is that there is an inseparable connection between our representation methods and our abilities to understand correctly abstract ideas/insights.

It means that the standard linear representation method actually prevents from us to deeply understand abstract thoughts, and new and better representation methods have to be developed, exactly as I did in this particular argument.

Any non-finite collection is incomplete by definition, as I clearly and simply prove in (and this incompleteness is represented by 0.000...1 where 1 is a permanent successor that permanently cannot be included in the non-finite and incomplete .000... sequence, and "..." does not mark our inability to write down a non-finite sequence of zeros, "..." actually says that any non-finite collection is incomplete by its vary own nature):

http://www.createforum.com/phpbb/viewtopic.php?t=39&...

http://www.createforum.com/phpbb/viewtopic.php?t=45&...

In other words, there is no such a thing like a complete non-finite collection.

You can say "show me a natural number which is not in N".

My answer to this question is very simple:

Natural numbers are defined by their axioms and the existence of each n in N does depend on how much n members are in N.

In other words, if we want to understand what a non-finite collection is, we have to deeply research the Successor concept, as I did in the above links.