If 0 was overspreading all numbers, what 0 could output in multiplication to any number must output 0 in no exception could be comprehended to us, but only the thing is never so enigmatic.

For instance, infiniteness must have two mutually very differentiated natures' presence.
One is necessarily, infinity and another is infinitesimal.

Infinity has no frame, though if we define category as what means only things which is having frame, necessarily only infinity must have been excluded as instinctive case.
Nevertheless, having no frame as situation could be comprehended by our mind, and that comprehension must be "one framing" in mind.
Meanwhile, inifinitesimal must be impressed as framed category, however if we set its meaning framed, we'd have another contradiction, because never framed thing must be somewhat we can define infiniteness in description. 

But necessarily between one number and anotherone, there's some categorizing devise, basically, infiniteness as being genuinely infinite must have condition in which any framed condition is exempted and if that could not be executed, any procedure must have been contradictory.
Then, necessarily, we must have conclusion that we necesarily need us have some another interpretation. That must be one set composing categorization and number's each sponteneously outputting gap between adjoined one must be arbitrarily configulated one expediency, if that interpretation could not be reasonably present, any mathematical number's arrangement must become only cotracdiction creator.

In other words, any number is expediently set up, or formed, then necessarily any number line in arrangement must be arbitrary, then necessarily inifinteness's nature could be obliged to be also so.
Thereby, necessarily infinitesimal between two numbers could be either arbitrarily set up one expediency.
That nature to some extent could have similarity toward infinity mirror, as kind of looking at oneself in two mirrors held against each other.

Hence, necessarily next truth must be outputted here.

Normally rerarded number line as arrangement (0,1,2,3,4,5,6,7,8,9,10,11,12,13,...) could be regarded only one phase as what we can confirm one wall's surface, and any divided each number necessarily makable line's outputting one layer, but each number's background has each distinctive width holding ow layer distributed previously, it could be either one layer.
In other words, normally our used number's line is one membrane or so, we'd say so.

That must mean multi-dimensional number's malable reality.

Because infinitesimal's nature must be contradictory at our vewing that framed exetent has own limitation, that number's arrangement must drag inifinitness's composite condition into contradiction.

Meantime, if we try to guide each crrosable layer into these cases, an ordinarily used our number linear arrangement arrangement (0,1,2,3,4,5,6,7,8,9,10,11,12,13,...) could be just one arbitrarily picked layer.
Then, necessarily e.g. if between 2 and 3, we could articulate extent's frame, just these are either arbitrarily configulated expediency as supposition.

In other words, consistently, only we have very inifinitely multiple layers, that kind of inifinitely deployable even with dimensionally deployable them are seen so necessarily each framable regulation could be only expedient, then, necessarily, deductively infinity and inifinitesimal in imcompatible contradiction as what no frame must be the absolute condition for setting inifiniteness.
In other words, at this phase we'd set arbitrarily, we for the first time the contradiction between inifinity and infinitesimal in gapped definition could be solved so well, for the present.

If we for the time being, could get these hypothesises could be correct, any numer's substantial natures with imaginary number, or so could be seen not contradictory, probably Kurt Gödel's Incompleteness theorem and Richard Dedekind's Dedekind cut could be comprehended with those my so rough sketched interpretable scheme.

And if we are asked ”What makes layer?", to it, for the present, now we should reply saying only "Our mind, necessarily for knowing arranged order, or kind of linear order's systematic mechanism.

One specified infinitesimal must have no framed state nor framed state, because one extent supposition could be arbitrary and interim opted by our mind.
And necessarily from the beginning, either infinity must have no framed nor framed state.

Though its nature could be applicable sample derived from one supositively deduced infinity.
Because both infinity and inifintesimal could be possible at embodiment with no framable conditioned premising.
Because either it could have necessity one suppositive upper limit as arbitrarily we could example at our utterance in lecture or explanation to anything, as "More than..".

                                     
                              
                                          SUPPOSITIVE LAYER's DIAGRAM
      　
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　　　　　　　　　　　　　THE SAME APPLIES BELOW.

（to be continued)

Jan. 6th.     2022

Memorandum; Infinitesimal could be interpreted with layer's idea, in solving contradictory dilemma, nevertheless, infinity's idea's essential enigmatic no framed or framable nature's signified truth as absolutely truth making identity is yet solved, we could regard so far.