THE FOURTHWAY MANHO EJOURNAL Volume 63 July 19, 2019 

MODERN MATHEMATICS AND THE STOPINDER NATURE OF THE SET OR CLASS THEORY By Professor Dr. Tan ManHo (An excerpt from the original work, Real World Views, Book 2 by Professor Dr. Tan ManHo entitled "Biocosmic NervoReflectant and the Theory of Material Reflection in Man, Inner Development and Social Upheavals", July 1972 ~ September 1973 Discourses, Chapter 7, Section C: "Modern Mathematics and the Stopinder Nature of the Set Theory", pp. 155~165)
C. MODERN MATHEMATICS AND THE STOPINDER NATURE OF THE SET OR CLASS THEORY
1
Back in the 1960's the modern mathematics, properly socalled has
ultimately proved itself to provide the exposition of the dialectic and
mentation by forms – nature is looked upon as consisting of discrete items
with distinct identity. The Soviets during its Golden Age of
Mathematics took the lead and the West badly needed to catch up – the sooner
the better. The general way which modern mathematics
handles quantities (but not as yet fully develop quanta) takes a peculiar
form, comparable to that used by a dialecticians in their listing and
categorization of the entities in the real world.
2
The Twofold ‘Expression’ Of Intersection Of Sets 1.
{a,b,c} ∩ {c,d,c} = {c}
[Method of selecting the common element] (i)
{Df,Df,Df,Df,Df,Df,Df} ∩ {Dw,Dw} = {D_{fw
,}D_{fw}} Df is a Day of a week which is fine weather Dw is a Day of a week which is windy weather [The case when the elements are the same in both
intersecting sets but of different qualities] In Df, f Є {D} ⇔ D = {f} In Dw, w Є {D} ⇔ D = {w}
In D_{fw,}
f Є {D}
and w Є {D}
or D = {f,w} If D stand for a fine day, therefore f, and w are
the two qualities of the element D. Є is an element of the set of days
(D)
(ii)
{P_{mtc,
}P_{mtc}, P_{mtc}, P_{mtc}}
∩ {P_{m,e,g,}
P_{m,e,g}}
= {P_{mtceg}, P_{mtceg}} if and only if the members of the second set are
the concluding set, the member of the first set to form the standard set. Criteria: i.
When intersection occurs between
two sets of the same elements, same in the sense that they (element) are
selected completely from a given standard set, the results gives a set of
the elements whereby each of which poses all the different qualities of the
two intersecting parent set, and whose number is determined by the smaller
set. e.g Standard Set: {B_{(f,h,b), }B_{(f,h,b)}, B_{(f,h,b,s)}}_{} Resolution into two sets and intersecting.
{B_{(f,h,b,s),}B_{(f,h,b)
,}B_{(f,h,b)}}
∩ {B_{(f,h,b,s)}}
= {B_{(f,h,b,s)}} B is the same element; f,h,b,s are qualities. Note
no repetition of f,h,b is allowed. ∩ is the symbol for ‘intersection’. ii.
{a,b,c} ∩ {c,d,e} = {c}. transposing, {c} = {a,b,c} ∩ {c,d,e} ⇔
{c} = {c,a,b} ∩ {c,d,e}
⇔
{c} = {c, L}
∩ {c, N}, where L and N are two sets not having common
elements. Also {D_{(f,w)}} = {D_{(f,w)}, Df} ∩ {D_{(f,w)}, Dw} Transposing,
{D_{(f,w)},
Df} ∩ {D_{(f,w)},
Dw} = {D_{(f,w)}} D is called the standard set of reference. e.g. D = {3
days of a week} = {D_{f, } D_{w}, D_{(f,w)}} Where D_{(f,w)}, L is called the repetitive members of the standard sets, or members considered twice in the two process. The repetitive members can have all even numbers for double intersection;_{} _{ } 2.
Venn Diagram (a)
{c} = {c,L}
∩ {c,N} _{ } (b) {D_{(f,w)}} = {D_{(f,w)},Df} ∩ {D_{(f,w)},Dw} E = D = Standard Set of Reference
e.g of 25 girls, 18 like pop music,13 like
classical music, and 10 like both. i.e.
{10G_{b}}
= {10G_{b},
8G_{p}}
∩ {10G_{b},
3G_{c}} 3.
Procedure To Comprehension [Building
up the whole through the parts] (A)
One is familiar that A ∩ B gives
C and concretely, {a,b,c} ∩ {c,d,e} = {c}. that is, the intersection of A and B vanish into
C….. now, given set C.
i.e {c}.
one makes a return to the original at a higher form. {c} = {c,a,b} ∩ {c,d,e} Now transform the subsets {a,b} and {d,e} into the
abstract into L and M, we have, {c} = {c,L} ∩ {c,M} where, L and M are sets which do not have any same
elements Note: This backward ‘Faustian Movement’ has its
utility where we deal with such problems: For example: There are 20 boys in a
certain class. 16 of them study physics, 14 study chemistry, and 12 study
both physics and chemistry. In this case, {c} becomes {12} = {12,4} ∩ {12,2} where A = {people taking both chemistry &
physics, people taking physics} B = {people taking both chemistry & physics, people taking chemistry} C = {people taking both chemistry & physics}
(B) When this has been done the construction of
Venn diagram is easier. E is the universal set to limit or give a name to
the set in reference. L,C,M is equal to the number of times different
selections are made on E. The Venn diagrams for {12} = {2,4} ∩ {12,2}
Since, E = {20 pupils}
Remark: G = {pupils wearing
glasses} and W = {pupils wearing watches}. G ∩ W is not well defined because
it is hardly known that whether there is a common element or not. If on the other hand, G = {pupils wearing glasses in the class, counted without respect to anything else not bothering about these with watches} and W = {pupils wearing watches in the same class, counted again without respect to anything else not bothering about those with glasses}, then G ∩ W has possible common element, if there is intersection, then realization occurs. 3 The relation between the old set theory and the new equivalent set theory, is as such that the old, much attributed to Boolean algebra of sets (George Boole) and Venn Diagram (John Venn), is algebraic, statistical and pictorial in its set to set relation whilst the new, due to application of Hegelian notion, etc, is dynamical and mentation by forms have found its way back into mathematics as a new complement of logical mathematical thoughts. The dynamical set to set relations from the low sets, i.e. sets with limited number of elements in them, up to the temporally universalis and its final finite and infinity nature of both the case in the set theory and the real world as it is. This is due to certain confusion about the universal set(s) — which often appears as the only universal set but as such is not and passes over into more universal sets and so on to infinity. This limitation and delimitation is a movement of the logical conception of universality of set. Discontinuities in the progression are subjected by the discontinuity intervals in the Octave of progression of set into its universality. The fact that a set must be transformed into a subset before it becomes a subset of a more universal set is inevitable, because by doing so, the transformedsubset presupposes the existence of a qualitative from of which this subset is only a belongingto or a “member” to another bigger qualitative subset which becomes the Universal set. Whilst the transformation of this first Universal set into a fact, universal subset presupposes a universality of a higher qualitative form, the second universal set, etc., etc. The inability to conceive motion, is apparently revealed when a teacher discusses the problem on the universal sets, the true significant of it is a formal logical habit of thinking has imposed itself on the dialectical and forms’ mentation in the head of the teacher. A common misunderstanding about limitation
and delimitation of universal set is expressed here. A set, {a, b, c},
is a subset of the universal set {a, b, c…x, y, z}. This limitation,
or rather first limitation is itself a set {a, b, c…x, y, z} and its
becoming of a subset of another universal set is unequivocally possible.
This set, can be the subset of another or rather the second universal set,
{a, b, c...x, y, z ,of English alphabets, a, b, c…x, y, z of the Chinese
Phonetic alphabet,…}, which consists of all known species of alphabets.
The initial limitation becomes delimitation and propels into more logical
universal sets – universality with boundaries to fence more dialectical
“notes” and mathematical “stopinders”, which still preserves the weak
oneness. (Dialectic, Stopinders and Sets)
