MATH a.k.a. Mathematics     Last updated on 2018/2562 6 27, a full moon day;

division operator; Also see: Operator IFF Mathematics; Radical286;

in Mathematics, relationship between 2 numbers is; Radical102;

Time . Space . Action: SYNC, ASYN, ... , Mathematics, some people like, some people dislike, you do not need several years of learning mathematics to know 5W1H of mathematics, but you may need a few hours of teaching from a genuine math teacher to understand all about mathematics; After understanding all about mathematics, and then time to do your ...  Do your own math, bring a common calculator, press 2, i.e. in ACT1 stage, and then press square root sign, and then keep pressing again and again √ square root 22 times, and notice that result prompts 1, and then try to mathematically prove that HOW a calculator slices time period, WHY only 22 times, WHERE is 2 * 7, and so on ... ; In Korea, average high school students can do math without using calculator, can perform up to 99 * 99; Try to compete math to Korea's new generation ... ; Try to compete, try to participate in the world's open math contests; Since 1985, 1 + 1 = 1 can be proved by algebra, therefore be very careful in equations, formulations, ... ;   The following information contents express the current up-to-date basic-understanding of mathematics;

2 inconsistencies in math are and problems of "cracks" WHICH kill symmetries;   Consider the image which represents dark, earth, sun altogether, this one & only the Sun [ just before noise in ACT2, the red line at top, visible by space imaging there is nothing out there except 4 planet prediction, just before dawn in ACT1, ... ] image might be the 1st crack of our universe's cracks, and yellow colored character represents the Earth, approx. 35+ years old information of the Sun in our universe; Only restricted people from higher civilization can solve ... ; The whole character Red + Yellow is king. And, notice that especially in this "the 1st crack of our universe", the gap exists, and the 1 gap might be for 1 tangent a@t 1 time of our universe a@t 1 dimension IFF dimensional hyperspace craft's retrospective in 1D. WHY red color as the 1st crack of our universe? Human beings perceive? also read Buddha Abhidhamma.

IFF problems of infinity exists (e.g.

floating points of square root 2 ≡ decimal expansion ≡ problems of infinity a.k.a. SQRT2;
floating points of square root 3 ≡ decimal expansion ≡ problems of infinity a.k.a. SQRT3),

use mantissa point doko WHERE truncating points are at e.g. (2^3) a.k.a. 8, (2^4) a.k.a. 16, (2^5) a.k.a. 32, (2^6) a.k.a. 64, (2^7) a.k.a. 128, (2^8) a.k.a. 256, (2^9) a.k.a. 512, 1K a.k.a. (2^10) a.k.a. 1024, (2^11) a.k.a. 2048, (2^12) a.k.a. 4096, (2^13) a.k.a. 8192, (2^14) a.k.a. 16384, (2^15) a.k.a. 32768, (2^16) a.k.a. 65536, (2^17) a.k.a. 131072, (2^18) a.k.a. 262144, (2^19) a.k.a. 524288, (2^20) a.k.a. 1048576, ... ; notice that C Sequence Number (structural) WHICH is beyond (dimensional, directional, numerological) starts at 2^20, 2^30, 2^40, ... ; also notice that 20 (i.e. middle JUN) water drops alike characters, inside the catalog of syllables (NIPPON, also see: Nippon Syllabary);

for each DEE (Dark Energy Engineering) pattern, DEE can be defined in mathematics, also see: Monbusho level knowledge enhancement 2, idea ♯ 216, defined DEE Patterns; for well trained kids! , you can define your own equations and formulations, ... ; good luck to you (e.g. you can have your own Gravity Dimension Computer, e.g. you can have your own imaginary hyper space crafts, e.g. you can have your own space system) ; notice that this DOMAIN has been designed, using graphics and keywords;

 Multiplication vs. Division (Any Number arithmetic) Method e.g. 90000 = 1800 * 50; 90000 = (1800 / 2) * 100; 45000 = 1800 * 25; 45000 = (1800 / 4) * 100; 22500 = 1800 * 12.5; 22500 = (1800 / 8) * 100; After understanding the above, develop Any Number, instead of "1800" ; Notice that "Division" seems easy, if compare to "Multiplication" ; Also see: Monbusho level knowledge enhancement 1, idea ♯ 180, Engineering Notation, and notice that log2 can be developed; regarding double entry book in accounting (NOT single entry), e.g. (5 columns at left side AND 5 columns at right side) As Ledger, so that left-and-right should be literally speaking "zero-and-zero" (balance equal) because, (debit entry at left, credit entry at right) As "Double Entry" (Remark: Double Entry Method is standard and well known accounting method); if I were CFO, or CPA, and found out that left-and-right prompts 72 different; so, I need to consult My AI system; HOW to trace the error (72 different) sir ? well trained kids! , answer would be numerological e.g. in numerological dimension, 72 and 27 are the same 9, but different is 45 = 72 - 27; the different number 45 is divided by numerological 9, e.g. 45/9, so that 5 is the number to be looking for the error (72 different), so that 2 integer combination numbers (i.e. regarding 5) are either 16 || 61, 27 || 72, 38 || 83, or 49 || 94, in this scenario; well trained kids! , now is the time, you need to figure other numbers so called Any Number ... ; And Then, name your own system; Remark: human beings' errors can be traced by advanced AI accounting system;

K-Theory and its D-branes, M-Theory and its strings, Unified Strings theory, ... , are all try to prove particles' vectors bundles ... ;

NCG, Non Commutative Geometry: common usages are "metric-tensor" to determine 2 points in space's length for each abstract notion of manifold, quantum field theory and its space-time, billions dollars cost so called non-trivial quantum relationship in commutation is NCG; Nuclear power of Western civilization was in 20th century only; To accomplish the ACT 2 stage, all nuclear power must be destroyed unconditionally; also see: worm=hole;

Super Symmetry & Super Gravity, must learn Chinese characters, because i.e. artificial energies, artificial lights, pressure machine engines, gravity machines, MRI(s) and PMD, remote-virtual-electricity, vertical EM scanner (s) and reflector (s), laser (s), ... , since 1980s ;

Characteristic classes, Fiber bundles, and Index theorems, ... , are related to dimensional space, hyperspace, ... ; Symmetry for each dimension; And very advanced, very limited, very classified, ... ;

Also see: Relational Algebra, RDBMS, since 1970s, along with index theorems ... ;

For basic understanding of WHAT is super symmetry, also see: Monbusho level knowledge enhancement idea ♯ 146; Super Symmetry;

Homology vs. Homotopy

Homological common usages are 1D circle, 2D circular disk, boundary, chains, homotopy complexes, simplexes, ... ;

Homotopy is a relation between 2 mappings; Homotopy common usages are contractibility, hole [also see: worm=hole], homotopic mapped loop, homotopy groups, loop, path, ... ; In Java language, 2 common mappings are JPA inheritance mapping, and JPA relationship mapping;

Remark: after understanding a path to be integrated, partially differential to each Left, and Right as a chain (s), and then try to understand 2-spin strings interaction, ... ; Also see: Pairs of sticks;

ACT2 and ACT3 objects are (2 and 3) vector directions, ACT2 and ACT3 2*5 JUN time, ACT1 and ACT2 (2*7) lunar co-existences [full moon day & no moon day, also see: \Info\Help\usamyanmar], ACT3 3 to 1 dimensions, ACT1, ACT2 and ACT3 4 planets prediction [2500+ years old information in Buddha calendar], ACT2 distance to SUN < distance to MOON, ... , and, ACT2 and ACT3 subjects are ACT2 2 times daily tidal water, ACT1 holes as no existence of the SUN (also see: no moon day), ACT3 horizontal and sectional gray scales [also see: \Info\index], ACT1 and ACT2 stars as no existence of the SUN, ACT3 very very very dark environment [also see: 4PP + JUN = 6, and 6 has been defined in Abhidhamma], ... ; Answer would be: the one the only the sun is gravity spot (please do not create gravity spot larger than the sun), and 1 way DEE and BF2 is because of our earth's momentum, and our earth is one of the moons, ... (also see: My Imaginary Space) ... ;

IFF (2*6) dimensional, also see: 8;

Differential Forms vs. Differential Geometry

Differential Forms: common usages are dynamics, integral-able conditions, ... ;

Differential Geometry: common usages are coordinate systems, covariant derivatives, metrics, curvature in coordinate, curvature in non-coordinate, ... ;

Lie Groups (also known as language of symmetry; also read the book: Page 103, Beyond Einstein, Michio Kaku and Jennifer Thompson, 1995): common usages are differentiable-manifold, killed vectors, lie-algebras representations, lie-derivatives, lie-matrix representations, ... ; Also see: 2-point distance to n-point distance;

IFF ACT2 ACT3 space mathematicians, also see: 2,3 dimensional distribution formula designing and engineering, [ for near future ACT2 space public traveling ... ];

O means Orthogonal; catalog groups of types into 7; 1 class is called O (N); atom itself is O ( 3); In 1800s, Sophus Lie (Norwegian) discovered a set of symmetries called SU (N) WHICH rotates complex number e.g. SU (1) with 1 photon, e.g. SU (2) with 1 photo and 1 neutron; Notice THAT prior to superstrings (1 word would be "spin"); (SU (2) x U (1)) with 1 electron and 1 neutrino; SU (3) rotates 3 sub nuclear particles; SU ( 5), the smallest GUT theory (1 electron, 1 neutrino, 3 quark); IFF N (quark) and then SU (N);  E (N) WHERE N <= 8 also known as E(8) group, and superstrings' symmetry begins, and higher dimensions begins e.g. 8, 10, 26, ... ; Unified Theory adapted Lie Groups in 1900s;

But, since 2000s, this DOMAIN has implemented (e.g. C Sequence Number) both 10 (2*5, dassa, 10, ... , dassa became desu thousand years ago) and 26 (numerological dimension) for thousands of years in software approach (hardware approach is intentionally left for oriental e.g. NIPPON; notice that Myanmar has been non-semi-conductor nation and this DOMAIN developer is out of hardware design knowledge e.g. HOW to embed Idea Processor into GPS ? e.g. HOW to embed GPS into computer? e.g. HOW to embed all basic calculator, dictionary, and translator to be AI ? ) e.g. web site as Triangulation System in the Internet, therefore, please do not change its aesthetics (also see: philosophy); Therefore, 21st century's power e.g. Gravity & IT, e.g. Manmade Global Weather (service), e.g. directional gravity for elevating automotives, ... are military top secrets ... , therefore, NOT available to public; WHICH is beyond stars are groups in constellations (also known as Lie Groups);

2100s predictions: gene therapy systems, gravity dimension computers, teleportation methods, ... ; There will be Rakhine (an ethnic tribe of Union of Myanmar) for sure WHO will ... ;

Analysis of Complex vs. Analysis of Real

Real: common usages are real function as isomorphism, real function as fix-point (s), and real function as mapping; Topologies such as neighborhoods, homeomorphisms, invariants, sets, ... ;

Complex: common usages are complex variables, space, strings representing as functions, surfaces, ... ; Also see: Complexity Region;

Probability & Statistics

Quantum mechanics in physics proposed, and demanded probability and statistics; Common usages are mean, quantitative counting of distinguishable objects, qualitative counting of distinguishable objects, quantitative counting of indistinguishable objects, qualitative counting of indistinguishable objects, variance, ... ;

Approximation Method

Fuzzy set was condemned in 20th century by western nations, but unofficially, however eastern nations accepted; In 21st century, so many proofs of so many new technologies make people around the globe convince that fuzzy set is the way to do controls; Whenever a problem cannot be solved, approximation method is needed; Large perturbation +, saddle-point integration, series' expansions in power, small perturbation -, ... are not in exact-closed-form, therefore, cleverly guessing of approx. ... ;

IFF distance approximation, also see: Monbusho level knowledge enhancement 1, idea ♯ 178, Distance Approximation with C Sequence Number, Math approach, HOW gravity spots as induction in 1 computer ... ;

Differential Equation: Ordinary vs. Partial

Function of 2 variables can be defined as y = f (x)   OR   x = f (y); doko WHERE y can be defined by function of x,   OR   x can be defined by function of y; IFF y = f (x) can also be written as dy = f'(x) dx, to do increment-approximation of the given function y = f(x) as d derivative of the function times  times = * = x = multiplication, ...  the increment of independent variable;

For example, d x = f' (t) d t means increment-approximation time t assuming that orbital synchronization time t of the given function i.e. x = f(t) as d derivative of the function * the increment of independent variable in 3-to-1 dimension as x,  WHERE in our universe, 3 planets' almost tangent valued gravitational waves cause 1 earth's full moon day ... ; In this case, derivative d t is partially calculated for partially delay time, partially artificial energies, partially artificial lights, and so on ... ; Also see: Time . Space's 3 for 3 dots in our universe ... ;

Algebra: Linear

linear equation must be express 1st, i.e. ai1 x1 + ai2 x2 + ai3 x3 + ... + ain-1 xn-1 + a in x n = c i; And then express the displacements either in matrices, or in vectors; Properties of abstract matrices are asymmetric, characteristic equation, determinant, inverse, symmetric, unitary, ... ;

Geometry: Analytical

Algebra and geometry; Geometric entities such as conic-sections, planes [such as: 2D plane, 3D plane, Polar plane, spherical coordinate, X Y coordinate, X Y plane, ... ], Sphere think circle in 2D becomes sphere in 3D, so called solid geometric entity, ... ; 5W1H algebraic equations for each geometric entity is called analytical geometry;

mathematical operators, also see: AI FONT;

Multiple Variables vs. Single Variable

Multiple variables' abstract functions, i.e. f (i, j, k, ...); Thus d derivatives becomes in partial, or/and, in a whole; In 2D, 3D space, integration of a path, integration onto a surface, are all based on directional d derivatives; Also see: evolute, and understand a curve's tangent (s) cause another curve, after understanding the directional d derivatives, partially or/and whole functionalities become designers' mathematicians' engineers' developers' 5W1H ...  concepts, ideas, logics, and so on ... ;

Single variable's abstract functions;

Transform: patterns can be transformed to-and-from between analog and digital; doko   WHERE analog is a.k.a. harmonic motion, and digital is a.k.a. discrete (isolated set of points ( dots)); Schematic Symbols' SHARP 's DAL e.g. , , , , , , , , ... ; transform e.g. (analog digital) also see: Fourier; pattern;

Trigonometry

Common usages are right-triangle (s), trigonometric functions of sine, cosine, tangent, ... ;

e.g. sin Θ, also see: 6sComputer;
e.g. cos Θ, also see: 1cComputer;
e.g. tan Θ, also see: 8tComputer;
e.g. csc Θ, also see: 7cComputer;
e.g. sec Θ, also see: 9sComputer;
e.g. cot Θ, also see: 2cComputer;

Geometry

2D, 3D, ... , Common usages are geometric shapes in 2D, geometric shapes in flat, 2D XY planes, similarity, symmetry, ... ;

Algebra

Linear equation of form y = ax + b;

Quadratic equation of y = ax2 + bx + c;

For advanced mathematicians only: solve and prove that the statement 1 + 1 = 1 can be proved by algebra, in a characteristic of Space . Action's 2-spin-strings, however, WHEN Time . Space concerns in ACT2, or ACT3 stages, HOW to prove 2 fuzzy sets { ... can also be proved as 1 f (x) of 1 fuzzy set { ... ; Question is whether Time . Space OR Timeless?

For Monbusho level developers only: 2500+ years old Myanmar's original document has been based on 7, and 2 * 7, in lunar orbits, 22 times of square root of 2, result prompts 1, mathematically prove that the 4 Planets Prediction diff in Space Time vs. Natural Time; WHY 22 times, HOW 2 and 7 relates to each other, ...

...

Basic mathematics Be very careful, since 1985, 1+1=1 can be mathematically proved by algebra

Analytical skill enhancement by studying relationship among point, line, angle, and plane; Parallel, NOT parallel proofs; Postulated parallel; Decision and reasoning skill enhancement of fuzzy logic, illogical logic, logical logic, relative truth logic, universal truth logic; Direct proof vs. indirect proof [Also see: ACT1 Theoretical Law To ACT2]; Triangle congruence, property, and similarity; Equality property of triangle vs. Inequality property of triangle; Equilateral triangle, Isosceles triangle, centralized triangle; ASA SAS SSS triangle congruence; Quadrilateral & polygon; Polygon property; Quadrilateral property; Area analysis of perimeter of quadrilateral; Circle vs. arc, angle, chord, tangent, ... ;

Linear equation vs. Linear expression; Slope form; Intercept form; Slope form AND Intercept form; Linear equation represents graph; Structure of Equation vs. System of Equation; Simultaneous equation & its Graph; Inconsistent system; Dependent System; Polynomial; Monomial vs. Polynomial; Simplified polynomial; Polynomial adding; Polynomial subtracting; Polynomial multiplying; Polynomial dividing; Polynomial pattern; Factor; Composite number; Prime number; Square number; Monomial factor vs. Polynomial factor; Diff of 2 square factoring; Quadratic equation, expression, function; Quadratic solution, by factoring, graphing, square rooting, squaring, formulating, ... ;

2D geometric figures; Point, and then displacement of points, Line; Plane & Coordinate; Angle; Triangle; Quadrilateral; 2D area vs. 2D perimeter geometric figure; Area vs. Perimeter; Unit & Dimensional Area; Parallelogram area vs. Parallelogram perimeter; Trapezoid area vs. Trapezoid perimeter; Circle, Cycle, Eccentric cycle; 22/7 circular part & its measurement; 3D geometric figures; Polyhedral; Platonic solid & sphere; Surface area vs. Volume [Balancing: non-object vs. object]; Dimensional state of solid; Symmetry vs. Balance; Symmetrical line & Tessellation; Kinetic motive rotation; Reflection, Glide reflection, and basic translational energy; [ACT3 coordinate-less D number];

Fundamental mathematical operations; Algebraic thoughts; Variables; Exponents; Large number vs. Small Number; Operational orders; Distributive property vs. Others; Integer; Coordinated integer graph; Integer's origin; Integer adding; Integer subtracting; Integer multiplying; Integer dividing; Absolute value vs. relative value; Real number; Rational number; Factoring; Squares and Square Roots; Irrational number; Pi is 22/7 [also see: ACT3 108 configuration & C108.GIF], pairs of sticks; Real number; Equation becomes structural by using variable; Solution oriented IQ enhancement by solving basic equations; Equation represents graph; Equivalent object balancing equation of LEFT = RIGHT; Algebra application; Ratio vs. Proportion; Area vs. Perimeter; Problem solving skill enhancement of time, distance, and rate, traditional concept of Time . Space . Action;

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