Are you relied upon by employers and applicants alike to certify you know what you claim to know? And you do realize there's a difference between being forced to pass examination to receive a diploma and having ideas forced on you?
Can you please show how I force you to agree with me?
You refuse to participate in a discussion that don't involve your ideas, and when you were allowed to post in the math forum, you attempted several times to take over threads where mathematics was being discussed.
If we use a structural point of view in this case, then 0.9999... is a one dimensional path of a base 10 fractal, that exists upon infinitely many scale levels that cannot reach 1.
0.999... is not a "one dimensional path". You've provided no definition of terms "base 10 fractal", "infinitely many scale levels". And obviously, since there is no definition available for these terms, you obviously cannot know that it "cannot reach 1".
Also we can say that 0.999... = 0.9+0.09+0.009+0.0009+... and we can clearly see that this sequence cannot reach 1.
What sequence? 0.999... is a decimal number. 0.9+0.09+0.009+... is an infinite sum (which equals 1, which can easily be computed from the fact that this is a geometric series) In any case, it is not clear that "this sequence cannot reach 1".
As you have not made any valid statements yet, you cannot conclude that 0.999... < 1.
Another example:
Please look at this beautiful Koch Fractal
http://members.cox.net/fractalenc/fr6g6s.577m2.html
Now let us say the there is a 1-1 map between each fractal level of 0.9999... to each different blue level of Koch Fractal.
0.999... is not a fractal, and I'm fairly sure there is no such term as "fractal level". Furthermore, you are merely saying (aka assuming) there is a 1-1 map between two things; unless you can show this assumption is true, you cannot be sure that any of your conclusions are true.
0.9999... = 1 if and only if we cannot find anymore a 1-1 map between some 0. ...9 to some Koch Fractal blue level
What is 0. ...9? And you've given no reason why this statement should be true.
Since Koch Fractal can be found in infinitely many blue levels and each blue level has a 1-1 map with some 0. ...9 fractal level, then we can conclude that 0.999... < 1.
Ignoring what comes before "each blue level", I think this actually logically follows from your previous statements. However, you've suggested no reason why your previous statements might be true.
Also we can say that 0.999... = 1 if and only if the outer contour of this multi-leveled Koch Fractal can be a smooth curve with no sharp edges.
You've given no reason why we can say that.
It is clear that the outer contour line is not a smooth contour in any arbitrary examined scale level.
It is true that the boundary of the Koch snowflake is not smooth. You've not given any definition of "scale level".
Again, this follows from previous statements, but you've given no reason to think those previous statements are true.
From this model you also can understand what is a "leap".
No, I cannot.
In short, any transition between a non smooth curve to a smooth curve, cannot be done but by a phase transition leap that also can be described by a smooth_XOR_no-smooth connection.
You've not provided definitions for "Transition", "phase transition leap", or "smooth_XOR_no-smooth connection".
This model is better than any "abstract" mathematical definition, which leads us to "prove" that 0.9999... = 1.
Better in what way?
Also by this "proof" we simply ignore infinitely many information forms that can be found in 0.9999... fractal.
Since there is nothing about the real numbers called "infinitely many information forms" nor is 0.999... a fractal, ignoring these is a good thing.
Now think how many information forms are ignored by this trivial and sterile approach of standard Matt (oops, Math).
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I can't, seeing how you've not said what you mean by "information form".