It is really so strange that the actual meaning of my question still hard to grasp for so many, despite the fact that it had been provided by me quite so many times in my few visible Q/A or my comments. Here at Quora, sci.math or MSE (where they deleted most of my contents without being able to refute them)

What is the maximum ratio of two successive integers? Ask yourself, let, [math] r = n / (n + 1) [/math]

As a common sense that everyone and layperson acquires, it is accepted that no two successive integers are equal (the proof is mainly common sense), as also confirmed by the many respected answers here, and of course this is perpetual (no matter however large is the chosen integers)

But top professional mathematicians around the world have objections, it is a quite long story, started since many centuries, current professional mathematicians had already inherited that peculiar discovery, which discovery?,

Every objection must be considered especially it is basically a mathematics problem, and simply not any silly problem, but the most important problem, actually it is the main protection wall of all types of numbers with endless digits (not necessarily being all as zero digits), after a decimal notation (in any constructible number system – base)!

But what is really the problem?, a layperson may asks!

It is quite simple as this, considering only positive integers, starting by substituting [math] n = 1 [/math], in increasing order, without a stop, and defining the ratio [math] r = n / (n +1) [/math], you would so simply get the infinite sequence as this [math] r = (1/2), (2/3), (3/4), … , 0.99, … , 0.999, … , 0.999… [/math]

So what did we ask?, the maximum ratio for [math] r = n / (n + 1) [/math], I suppose!

So it is so obvious for a layperson now that the maximum ratio [math] r = n / (n + 1) = 0.999… [/math], when (n) is large enough and tending to (what they call it, infinity)!

But it is widely and commonly believed and well established among top professional mathematicians (with hundreds of alleged proofs) that [math] 0.999… = 1 [/math], therefore [math] n = n + 1 [/math]

A fact that took many centuries by the most top famous professional mathematicians to be well established, It opened the doors so widely for the professional mathematicians to produce infinitely so many theorems, so many puzzles, so many fictions, … etc, (so unbelievable),

It is not only this fiction, but also so many others, you would not believe, starting from the misuse of negative numbers concept, to create the fake imaginary complex numbers, to non Euclidean geometry and many fake positive real numbers that was proved rigorously impossible numbers since many centuries ago by Euclidean (so unbelievable)

So, what a layperson can do in this case, believing his own natural common sense or shrugging it as had been decided by the top brain masters?

But the brilliant and clever students cannot shrug it so easily, once they realize the fictions in mathematics.

I had conducted a kind of little personal research and discussions on those topics with other gradated disciplines, where I concluded that (those issues called advanced mathematics) don’t mean anything to them, but truly many of them like the old mathematics, It is luckily that those topics seems nonsense to the majority of many educated people from different branches as engineers, they simply consider them as wasting of time, being also unaware of their harmfulness on the human minds, because they lack the coherent logic that old mathematics do

But the motives of all those fallacies rarely started innocently by the [math] \pi [/math] deception, and later intentionally starting by inventing the cube root of (2), just to pass unnecessarily talents and were a kind of pure business that was based on corruption

Finally and not last, if we keep the mathematics expanding freely ungoverned (not by gravity), but only by the number line, I swear, the future volumes (say in the next century) that would be created by the baseless, fake mathematics would need a galaxy size to store, whereas the original whole real meaningful mathematics can almost be stored in few books only!

Thanking your patience and tolerance of my opinion in this regard

Bassam King Karzeddin

29th, Oct., 2016