Again, wiki transitive property first before going-on:

http://en.wikipedia.org/wiki/Transitive_relation

Then, in binary relationship of a cartesian product (C) as square matrix,
the relationship is transitive when the following operation occurs:

A relation R on a set A is called transitive if whenever (a,b)  R
and (b,c)  R, then (a,c)  R for a,b,c  A

Let's look at a simple example C:

The above relation is NOT transitive because:
(2,1) & (1,2)  R but (2,2) NOT  R

In the MBTI algorithm to be discussed,
it is of utmost importance to know the intuitive method to identify transitive property.

Note the yellow lines - the intersection point of lines is of transitive property.

Case 1: (1,1)

The 2 lines contains at lease one element each and has intersection on both sides

Case 2: (1,2)

The line/row x=2  has intersection BUT no element off-intersection on right side!
The line/column y=1  has intersection BUT no element off-intersection on down side!

Need not to do case3, as there already has a counter-example
to disprove the transitive property of C!

Your turn (5 mark):

Prove that R={(1,3)(2,4)} in 4x4 square matrix C is transitive.

(2112-onward HKCEE Pure Mathematics Paper I (Algebra and Namespaces) - Section A

Now we move on to MBTI algorithm of computing foe types.

Here is an example of computing ENTJ's foes.

It can be seen that ISFP's foes are the same as ENTJ's.

R={(ENTJ, ISFP, INTP, ESFJ)} in 4x4 square matrix C is transitive
because any 2 combination of elements in the yellow line/
pale blue box can result in ENTJ, even if the elements are not real.
It is because the unreal 2 elements NOT  R1 use parameters   C
You should able to notice that the separation between elements
in the yellow/pale green lines is once-consecutive elements.

Actually we can use psychological functions to prove the algorithm.

Your turn (70 marks):

By using compact relational database software Microsoft Access,
turn the 6 MBTI Type as entites and thus 6 different tables,
then compile the SQL command using EXISTS(cmd) function
to verify an instance that ENFP like INTP.
Your cmd should have 2 forms:
1. use subquery
2. join tables
Write BOTH of them.

How many marks do you score from the 3 turns then?

40-64: PASS
65-74: Credit
75 or above: Distinction
39 or below: Fail

Now you know a bit as to how computer sciences can like up with social science.

If you don't know how to get the answer by psychoanalysis, read further: 

萌系ACG狗公 qooalex83 (愛理大叔) 肯定有看過以下reference的日文版:

原來, 這狗公在另一狗公CUHKACS 吳偉明 (Ben Ng) 鳩吹的一詞「弦外之音」,是:
他們寫論文時「天下文章一大抄」,
當事後孔明(hindsights)!

Therefore, I have to show the source of their so-called
"thesis" in order to unveil they 2 "dogmen" (bastards)
as hideous copycats!

 Not quite understand? Go on read read read...

下次看不明我(ojalyticianist/amateur Jungian psychologist)的文章後,
一知半解想用「精神分裂」標籤當籍口老屈我 psychotic 時,
make sure you make clear of the meaning of 「多重人格」,
否則小心你最後因不斷搵我「過橋」製造猜忌而患上精神病, 自食惡果!

陶傑倒也棒的, 能夠指出成龍評中港台的 rationale.

Wiki the following first:
http://en.wikipedia.org/wiki/Fundamental_attribution_error
Then you will know if your judgment
on Jacky Chan's speech is politically correct.

因此, 為方便中港台的人能認清事情多方面,
我 quote 了以下陶傑在2009-04-24的文章作日後參考:

First, we need to choose those personality inventories  that disallow odd-numbered choices.

So it is not worth doing psychometric test of the following format. (i.e. accuracy)
Here is an instance (http://similarminds.com/cgi-bin/newembj.pl)

One can bypass the decision making for any unfamilar items,
thus they probably fill the middle option as default option.
Then, the analysis, since middle option has empty preference,
will become inaccurate because no boolean values are available
for checking preferences.
Hence, I only choose those inventory with even-numbered choices,
since for an inventory to be effective, one must ensure that
the question deny omission of perference orientation.

Thus, for MBTI, I can only find a WWW test with even-numbered choices.

http://similarminds.com/jung_word_pair.html

Here is my result to certify tendency of preference by percentage,
and the test, although informal, managed to compute the correct MBTI type.

Length: 61 minutes

http://sites.google.com/site/aikosunoo/Home/p24.amr?attredirects=0

Some call my oneself podcasting as psychotic,
and judge if I am a geek by counting how few no. of friends I have.
Here I will declare this puzzle and explain what otaku engineering is as well.

Note: Theory of MBTI will be used again and again.

Length: ~33 minute

許多與我思想相左的ACG迷 (eg. 狗公 Defender) 和舊同學 (e.g. 林春艷),
心中有共同但單一的願望: 妄想要我收皮, 掛掉我這個 blog.

現在, 我同時帶給它們好消息和好壞消息:

好消息: 為了 Assigment, Test, Examination, 和開展主流高中試卷研究,
我必須從今天開始閉門自修, 休養生息, 直至期考在六月尾結束為止。
現在你們暫時不用擔心我會在此時此刻狂開 post 玩批鬥。
相信狗公吳偉明知道此消息後, 一定會開心到日日出資訊娛樂化 post,
垃圾動漫迷見到烏大龜初夏休眠, 有「佳」「福」了~

壞消息: 我只是說我不會在期考結束前發 post,
不代表我不會看別人的 blog, 取其戇鳩內容備分, 方便試後批鬥;
此外, 我閉門自修期間將會大量閱讀學術書籍(尤甚是預科經濟學和中國文學),
同時以 CD-ROM 的形式閱讀其他人的 Web 2.0 產物,
好好增值自己。想在沒有學科技術背景的情況下取我blog文為樂? 讀EVCHK歷史吧,
我現在可沒有時間倍班垃圾動漫「狂」迷一起「瘋」啊!
不用問, 試後的批鬥偽君子之舉將會更 advanced, 務求它們鬥志盡喪!

至於更新暫停的根本原因:
現在我 formal 的 OJA STUDIES 試卷問答基本上已經 implement 哂; 同時,
直到目前為止我發出的未來文章已經達到半年產量了 (up to 2009/10/30 ),
所以我的讀者想消化文中我的思想, 恐怕需要一大段時間,
而且 google tag 我 blog 文的速度暫時追不上我寫 blog 的進度,
因此, 相信這接近兩個月的 gap time, 能讓有心人一口氣 study 我三千多篇全文吧!

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There is lots of application of doremotional progression.
The benefit of using doremotion progression is that,
you can customize preconditions and postconditions for a particular proof.
Doremotional regression is also a form of doremotional progression,
but the difference is that, doremotional regression will turn out more
than 1 outcome. In life examination paper of OJA STUDIES,
we rarely require a candidate to use doremotional regression,
because this section is inside Syllabuse A which is for arts stream students,
and doremotional regression requires advanced mathematical skills
which are out of their capacity; what's more, the concept of
synchronicity must be required since doremotional regression is NOT
a function, i.e. doremotional regression is one-to-many.
Therefore, a question of doremotional progression may require you
to find axioms as partial doremotonal regression. Be aware when
considering which one approach or both should be used in proof,
no matter the nature is algebraic, geometrical or literal.

Here is an simple application of doremotional progression
with minor doremotional regression requirement that can tell you
how to make a model for custom theories (in this case, konics[受相學]).

Exception: The above proof assume that introverts has Ω>0
But in reality, since dissipation of psychoanalytical energy exists,
Ω<0 is also possible for introverts (i.e. introverted sensing),
but the proof in the flashpaper means that Ω is permanent factor.
Hence, the "impossible case" actually means temporary cases.
For ISFJ, ESFJ, since they actively use introverted sensing,
so the exception occurs periodically. Note that reality is an
OPEN system so psychoanalytical energy is NOT conserved.
Hence, an dogman of ISFJ using introverted sensing does
not mean that his dissipated energy (Ω<0) is offset by
reducibility. Instead, it is flown to aikolises.
(e.g. His sexual motivation triggers kong-gals utilitarianism,
i.e. introverted thinking as a void energy-influxing function).
Since the above proof is assuming conservation of
psychoanalytical energy for an individual,
so the actual assumption is that (E-I)‧E >0

So to be precise and exception-free, we better use summation
to allow offsetting of exceptions, i.e. for introverts, 
∑ Ω >0 for all Ω  of any scalar values

In sum,
the exception explains phenomena in reality
as to why dogman, although introvered,
get aggressive after puberty.
(Because all these ISFJs of 95%
of total population are going to woo girls!)

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The synchronicity instances are of single inheritance.

So if more than one inhertance is required to generate synchronicity,
we will describe the instances as polyjective. In this case,
we call the instances as of multiple inheritances.

It is common in C++ Programming (Note: Java allow only one inheritance.
Therefore, for certain D.R., we need to generalize more than 1 thing.

Here is a Polyjective Regression Modeling using UML:

Sample Problem:
By doremotion regression,
prove that an human relationship hegemony must involve at least one:
a. Kongrill (港女/狗公), AND
b. Traditionists (SJs in Keirsey Temperament Sorter)
(Hint: a and b are NOT equivalent)

Sample Solution to the problem:
Kongrill can be non-SJs, say an INTP.
An example is Onpu Segawa in the anime Ojamajo Doremi.

Onpu Segawa is a showbiz starlet so she has to maintain her fame
for livelihood. Hence she needs to use emotive means to shape
the support from her fans. By her dominant introverted thinking,
she will be utilitarian. Then by her auxiliary extraverted feeling,
where dominant in ESFJ (a traditionlist sub-class), she will learn
more and more appealing acts by mimicking. For example,
she may learn to copy the following hairstyle that improves her self
human capital (appearances) to outwin other starlets:

i.e. making herself doll-like to trigger sexual appeals as
introverted sensing, which is dominant for ISFJ (another  traditionlist
sub-class). Henceforth, Onpu Segawa will gather certain male fans
(the male fans are mainly ISFJs with sexual motivations). Then,
Onpu Segawa can manipulate on other relationships by spreading
intended ideologies to her friends. (e.g. to blacken another starlets'
names). This results in competition between human relationships
and those who is less competent than Onpu Segawa will lose
in the showbiz market; therefore, human-relationship hegemony thus exists.

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Consider Shoes (A)<=Butterfly Knot (B) =>Lolita Dressing Style (C)
Then we classify synchronicity: A and C.
Usually a doremotional regression starts from A then C or C then A,
then backwardly derive B.

Example:
By doremotional regression (D.R.),
prove that common dogman is ISFJ.

Clearly Common dogman is a synchronicity. Then we need to find
at lease one more synchronicity to derive ISFJ postulate.

The methodology is that, we prove another case having ISFJ attributes.
The case will be another synchronity. So things make simple,
doremotional regression can be transformed to doremotional progression.
Then the question is equivalent to:
By doremotional progression, prove that XXX is ISFJ.
XXX can be anythings that manifest the preconditions of ISFJ.
That is, the non-synchronicity component in an D.R. question is right
postconditions for XXX and common dogman as synchronicities.

Bear in mind that XXX never equals common dogman,
because we are NOT performing inverse function or analogy.

Hence, we can put XXX as another non-A items having ISFJ properties.
Note that we cannot say that "XXX is ISFJ" as a proof because
this statement is already set as conclusion in the question.
So never say such a tautology!

So how can we solve this D.R. question?

Here we will use Chinese to compute the proof:

常見的狗公大多性欲強.
Ewai_leong 和 Defender 皆為常見的狗公
他們偏重性暗示式萌 (e.g. GL, Strike Witches),
所以他們的潛意識為 sexual motivation
所以, 他們大多是衝動的.
在 Rozen Maiden, 女角真紅(Shinku)也是衝動的,
而且喜歡其後濫用價值判斷貶低其他女角的尊嚴
因此, 真紅和常見的狗公有共同的特徵,
就是他們衝動的本源是,
而他們衝動時大多使用(價值判斷).
根據 MBTI, ISFJ 的定義是先內向感覺, 後外向情感
因此, 我們同時證明了常見的狗公和真紅是ISFJ.

Hence, we can see that D.R. is actually initiating multithread inverse
from theorem to experiment, to experiment to hypothesis,
from hypothesis to postulate, from postulate to axioms.

Thus, remember the key to D.R. : Back to definitions.

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[Anti-]Phase distribution is used instead of normal distribution.
Phase distributions use logistic functions.

Mathematical Expression:

In OJA STUDIES, we use the area covered to determine
probability density of a person's IQ for the range 100-200.
(Note t=standardized σ )

The distribution of IQ, where the function is probability,
 is thus -P(t+6) (i.e. it is antiphased)

So how can we know the probability of finding people of IQ>115?

(1 + ln(2)) / 12 = 0.141095598

That is, the population of talents X~14%.

If we use normal curve analysis in the theory of toitoise instead,
Talents population = (Male Talents + Female Talents)/200
=(Male(IQ>130) + Female (IQ>115))/200 = (5+32)/200) ~ 18.5%
But (Male(IQ>130) + Female (IQ>130))/200 ~10/200 = 5%
Hence we can compute the result which is consistent with X that,
nearly (X(~=18.5-5)-5/2%) = 11.5 in 100 females are kongrills (港女) of 115With reference to MBTI statistics:

ISTJ 11.6%	ISFJ 13.8%	INFJ 1.5%	INTJ 2.1%
ISTP 5.4%	ISFP 8.8%	INFP 4.3%	INTP 3.3%
ESTP 4.3%	ESFP 8.5%	ENFP 8.1%	ENTP 3.2%
ESTJ 8.7%	ESFJ 12.3%	ENFJ 2.4%	ENTJ 1.8%

 

We can then conclude that, besides ESFJs,
(12.3-11.5)% = 0.8% of kongrills are INTPs/ISFJs.

Further references: http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/moreApps/logistic.html

Further practice: Prove that male ESFJ/INTP population is 2.3%.

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Here is another case of doremotional progression.

Note that in this case, the concept of "absolute" is introduced.

Without "absolute" as modifier of a function,
we are unable to perform D.P. analysis of divergent functions.

Now, if you are an arts stream(文科) student, stop rote-learning here and 
don't be hestitate: buy and read HKALE Pure Mathematics textbooks,
since OJA STUDIES will use many mathematical concepts that are out of
HKCEE [Additional]Mathematics syllabuse (e.g. domain)

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Doremotional Progression is [in]finite series of positive real elements.

The definitions of doremotional progression will be shown at the bottom
section in this post (i.e. the Flashpaper document) 

It is of the following use:

1. Tracing the trend of marginal returns (i.e. increments)
Some say that marginal return is d$/dt, i.e. slope of return function.
This is a WRONG concept because he/she considers Δ$/Δt=d$/dt.
An example to illustate the difference is y=Ne^-x
dy/dx = -Ne^-x<0,
but Δy/Δx = Ne^-Δx/Δx >0
(Note: In a positive x-axis, Δx = x2-x1 > 0)

2. Finding out the preconditions of a particular case.
Doremotional Progression (D.P.) is like reverse engineering,
which is usually to trace out the hidden domains/variables/constraints
under a given case to be proved.
For example, if you are required to use D.P. to prove the following case:
"Girl is smarter than Boys in langauge"
You cannot manage the proof if you don't know the preconditions
that girls use langauge centre of left brain intensively. To finish D.P.,
you have to use the preconditions iteratively to complete the case.
Usually, D.P. is many(-preconditions)-to-one(-case), but the reverse
is possible. In this case, the D.P. will have another class called
doremotonal regression (D.R.). D.R. is one-to-many.
That means you have to perform tracing of axioms (an e.g. of preconditions),
or performing case study by sociological imaginations,
i.e. doing query for postconditions.

Hence, D.P., unlike other progressions like A.P./G.P./H.P. (harmonic series),
can be used to handle mathematical functions of even wholly literal form.

To make the concept simple, here is a sample application
using the simplest form, i.e. mathematical expression.