Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages.
Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasize concepts for computer science majors.
For me this becomes the question that is highlighted in bold as to such a thing as discrete mathematics being suited to the nature of the Quark Gluon Plasma that we would say indeed that “all the discreteness is lost” when the energy becomes to great?
Systemically the process while measured in “computerization techniques” this process is one that I see entrenched at the PI Institute, as to holding “this principal” as to the nature of the PI’s research status.
Derek B. Leinweber’s Visual QCD* Three quarks indicated by red, green and blue spheres (lower left) are localized by the gluon field.
* A quark-antiquark pair created from the gluon field is illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton.
* The masses of the quarks illustrated in this diagram account for only 3% of the proton mass. The gluon field is responsible for the remaining 97% of the proton’s mass and is the origin of mass in most everything around us.
* Experimentalists probe the structure of the proton by scattering electrons (white line) off quarks which interact by exchanging a quantum of light (wavy line) known as a photon.
Now indeed for me, thinking in relation to the 13th Sphere I would have to ask how and when we loose focus on that discreteness)a particle or a wave?). I now ask that what indeed is the fluidity of the Gluon plasma that we see we have lost the “discrete geometries” to the subject of “continuity?”
So the question for me then is that if such a case presents itself in these new theoretical definitions, as pointed out in E8, how are we ever to know that such a kaleidescope will have lost it’s distinctive lines?
This would require a change in “math type” that we present such changes to consider the topologies in expression(this fluidity and continuity), in relation to how we see the QCD in developmental aspects.
In a metric space, it is equivalent to consider the neighbourhood system of open balls centered at x and f(x) instead of all neighborhoods. This leads to the standard ε-δ definition of a continuous function from real analysis, which says roughly that a function is continuous if all points close to x map to points close to f(x). This only really makes sense in a metric space, however, which has a notion of distance.
Note, however, that if the target space is Hausdorff, it is still true that f is continuous at a if and only if the limit of f as x approaches a is f(a). At an isolated point, every function is continuous.