Concepts and Numbers
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Concepts and Numbers
Alphabetical language and mathematical language

The same as to express and to define the elements that surround us we must use of an alphabet of letters and a vocabulary of words, phrases, sentences, phonetic expressions, etc. to which we call language, which allow us understand to be defined these elements according to their different qualities, in the same way we can also use another language type with another types of signs (the numbers) that allows us to understand the elements that surround us as for their quantity and relative dimension among them.
Therefore to the group of numeric and mathematics expressions we can also call language, in this case, mathematical language.
Because well, in the mathematical language the signs to use are the numbers, which are orderly and they match with a scale of values taking as reference to the unit (1) and whose main finality is the valuation and appreciation of the elements according to their quantity and dimension.
Therefore, the mathematical language is a specific way of expression and understanding of the elements that surround us.

In this same sense, and going a little into the metaphysics field, we can say that the same as in the evolution of the alphabetical language we get high marks of linguistic development ending up getting beautiful poetries; complete explanations and dissertations; sensitive novels and stories, etc., with the development of mathematics we end up understanding, gauging and feeling in extensive and wide form all those that surrounds us.
Certainly we could compare a beautiful poetry from the alphabetical vocabulary to a beautiful demonstration or theorem of the mathematical alphabet.
In fact, both languages are ways of understanding, to feel and to express all that we have within our reach or in our mind.

Reason of being of numbers

Let us suppose for a moment that before being created the Universe, an intelligent but incorporeal being had been created, which would be therefore in an empty space without any element or substance that can be observed.
In this circumstance we could wonder if this being could begin to learn and use the numbers and the mathematics if nothing exists around where it can use the numbers.
The answer should be clear: No, of course.

Nevertheless, if later on many things were created in the Universe such as stars, suns, moons, etc., then this being would already begins to realize that would be necessary the invention of a code or numeric alphabet to be able to assimilate mathematically the quantity of elements that now could observe.
This tells us that so we need a numeric alphabet, previously we need of physical elements on which we can apply these numbers.
Therefore, and to study the numbers we go firstly to revise a little the properties y characteristics of the physical elements, and for it, we will study their main substantial characteristics:

Substance:

Substance will be considered every existent thing that has physical or conceptual character.
--- This way, in the Physical Universe, it will be substance everything that contains space, time, energy, mass, forces, etc., as for example water.
In the conceptual field it will be substance any concept type, sensation, intelligent definition, etc. that can be conceived by any human or animal being, or even that you can consider that the Cosmos contains for itself, as for example the physical laws.

Entity:

Entity it will be all physical or conceptual substance that is conditioned by an extension, situation or development ambit.
--- In this case, to our mind we can consider it as a conceptual entity located in our brain.
--- In the same way the water of a lake can be considered an aquatic entity to be located in a certain place of the space.

Compact:

Compact will be any entity in which we can't or we don't want to distinguish their possible parts or components.

Integer:

Integer will be all entity to which we consider complete when doesn't lack nor has surplus any of its possible parts or components.

Independent:

Independent will be all entity that is located, defined or considered far or apart from other entities.

Element:

Conceptual element will be all entity that we consider as compact, integer and independent to the effects of the studies and applications that we are carrying out.

Univocal:

Univocal will be those elements to which we consider them with the same nature, value or consistency so some can substitute to other for the finality or studies that we are carrying out.

Unit:

Unit will be any element that we consider compact, integer and independent to take it as base or pattern to compare, measure and to study to all the other elements that we consider univocal among them.

Set:

Set will be when more than a unit of compact and integer elements exist, but when being near and gathered among them, we can consider dependent some of others for their proximity, cohesion or special functionality.

Multiple:

Multiple will be all group formed by units of univocal elements.
In it, we accept mathematically the inclusion of the groups formed by a single element.

Number:

Number will be the signs of the mathematical alphabet, all them distributed in a scale of values with relationship to the unit (1) that are good us to understand and express mathematically to any entity.

Measure:

Measure will be the consideration, valuation and numeric expression of any entity in relation to the unit that we have established for this entity.

Quantity:

Quantity will be the measure of any entity.

Multiplo:

Multiplo will be the quality of multiple, but extending the gauge to any quantity of the substance to measure, as much units as part of units.

Number's chronology.

When we refer to the number chronology, we are referring to how the living beings and mainly the man could go conceiving and assimilating to the physical elements that surrounded them by means of the numeric or mathematical language.

To make us an idea of how the animals and later the humans could understand and go assimilating the necessary numeric principles, we could think in the hypothetical experiences of the ancestral animal and the posterior man development.

For this, we can ask some questions:

What primary concepts would begin to nest in the brain and mind of the animals?

I think that possibly the animals would begin to have simple ideas of the different substances and elements that surrounded them.

For example, the water that they need to drink could be "sensed" or assimilated as a kind of necessary substance for the life.
Likewise the fruits to eat would be also necessary elements for its sustenance that they could assimilate as compact elements.
And surely, they soon would "understand" that the elements within their reach could be in solitary, that is to say, one; or they could find them forming groups, that is to say, several of these elements.

Therefore in the primary animals they could feel already that alone elements and gathered elements existed.
So they could have a very simple idea of what were elements and groups of elements only; of what were units and multiple units alone.

But surely many thousands of years should pass until some simian, a little more intelligent and onlooker would try to distinguish and differ to those multiple units or groups among them, according to the number of units that this groups had.

And probably here went where began to be born and to be kept in mind to the mathematics of the elements.

Probably everything began with the simplest things:
If our simian joined two fruits to eat, he would realize that he had something more than alone one, and he would inwardly already give a meaning or understanding of this group of two elements.
Then he would make it with three, four, etc., and with it we would be already our simian-man entering in the field of the natural numbers and of the countable system.
Therefore, the natural numbers concept began to be conceived and understood a lot of time after than the unit and multiple ideas were born in the animals mind.

Now then, with these antecedents we can already give a definition of what is a natural number using the idea of accumulation that our simian or primitive man used for the understanding and use of these natural numbers:

Natural number

"Natural number will be all those that we can obtain adding units."

Or

"Natural number will be all multiple of the unit (1)."