The Continuum

" The Continuum TEC Technics

We use the terms "existence" and continuum frequently here at TEC Community, so let us briefly explain their contextual usage. Aristotle proposed four categories for the many meanings of "being":
(1) Being in its essential and inessential senses
(2) Being in the sense of the true
(3 ) Being in the sense of potentiality and actuality
(4) Being in the various senses derived from the schema of the categories.
A common thread in all of these categories is that their members are manifestations of "energy". So, in TEC Community, the being of interest is "energy". There is an infinite number of "configured energies" in Space-Time. Each configuration establishes its unique identity. All universal concepts are implicit in Space-Time, especially the containership property of space and energy, the primary universal concepts that initialized Space-Time. We brought the universal concepts that consitute SED out of the Space-Time contiunuum, in order to explicitly emphasize the importance of their existential role.

"Continuum" is Latin for a "continuous thing". So what is the meaning of a "continuous thing"? Consider an individual who is walking from point A to point B.
A_________________B If this individual does not stop at any point between A and B, his/her walk from A to B can be considered to be "continuous". So in this sense, "continuous" implies "no stop", and the distance AB can be considered to be a "continuum" of this individuals walk from A to B.

There are many other everyday examples of this simple conception of "continuum".

Mathematicians have a more rigorous "no jump" definition for "continuous". They approach the "no jump" notion in three steps:
(1) They conceptualize a curve as being made up of innumerable points
(2) Then they focus on one of these points and define "continuous" with respect to this point
(3) Then they apply this definition to all the points of the curve and by so doing, define "continuous" for the function.

Let x be the point of interest (x is a variable whose value is taken from a stated domain). Now conceptualized a left neighborhood of x ( a region immediately to the left of x) and a right neighborhood of x (a region immediately to the right of x). Let us choose two points "a", "b" sufficiently close to x ( "a" is from the left neighborhood of x and "b" is from the right neighborhood of x). Mathematicians say that a function f is continuous at the point x if by choosing a and b sufficiently close to x, they can make the value of the function at a [f(a)] and the value of the function at b [f(b)] as close together as possible. Then they say that the function f is continuous if it is continuous at all points x.

So, the mathematical definition of continuum is implied whenever we use the term continuum. Consider for an example, the Knowledge-Information Continuum. When we apply the "no jump" notion to the continuum, we mean that the bodies of knowledge that constitute the continuum are seamlessly connected. Unconnected dots does not imply discontinuity rather they imply that the connecting bodies of knowledge are yet to be discovered.

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