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This is more understandable than the Wikipedia entry.
WHAT IS MATHEMATICAL MODELING?
Mathematical modeling is the process of creating a
mathematical representation of some phenomenon in
order to gain a better understanding of that
phenomenon. It is a process that attempts to match
observation with symbolic statement. During the
process of building a mathematical model, the modeler
will decide what factors are relevant to the problem
and what factors can be deemphasized. Once a model
has been developed and used to answer questions, it
should be critically examined and often modified to
obtain a more accurate reflection of the observed
reality of that phenomenon. In this way, mathematical
modeling is an evolving process; as new insight is
gained, the process begins again as additional factors
are considered. “Generally the success of a model
depends on how easily it can be used and how accurate are its predictions.” (Edwards & Hamson, 1994,p.3)
M > T
T > ~D
~E > G
E > D
———
.: M > G
================================
M = making money, T = takeout food, D = dinner, E = everyone, G = getting food
If you are making money then it implies takeout food.
Takeout food does not imply dinner.
Everyone does not imply getting food.
If you are everyone then it implies dinner.
—————————————–
If you are making money then it implies getting food.
_____________________________________________________________
The word blog refers to the word weblog.
There is no proper English in the word blog.
All proper English is understandable.
—
What is not understandable is the word weblog.
B > W
~E > B
E > U
————
.: ~U > W
The Oxford logician and author of Alice in Wonderland, Lewis Carroll……..
===========================================================
These are Four Riddles from Lewis Carroll inspiration.
–
Read these articles:
Lewis Carroll Logician and Mathematician
Carroll’s Paradox
First, visit — Monty Hall Problem. Don’t read past ‘Solution.’
Attempt to solve. Write down method of solution.
Read ‘Solution.’
Visit Wiki’s Monty Hall Problem.
Carry out ‘Simulation.’
—
It is hardly easy to understand this author, but here is a PDF.
There is a nifty calc on stattrek.com
And then here is site relating to poker hands.
This PDF on Ace Distribution is somewhat readable.
What is the difference between the two?
Another explanation from Britannica.
Set Operations (A Wiki Rip)
There are ways to construct new sets from existing ones. Two sets can be “added” together. The union of A and B, denoted by A ∪ B, is the set of all things which are members of eitherA or B.
Examples:

 {1, 2} ∪ {red, white} = {1, 2, red, white}.
 {1, 2, green} ∪ {red, white, green} = {1, 2, red, white, green}.
 {1, 2} ∪ {1, 2} = {1, 2}.
Some basic properties of unions are:

 A ∪ B = B ∪ A.
 A ∪ (B ∪ C) = (A ∪ B) ∪ C.
 A ⊆ (A ∪ B).
 A ∪ A = A.
 A ∪ ∅ = A.
 A ⊆ B if and only if A ∪ B = B.
[edit]Intersections
A new set can also be constructed by determining which members two sets have “in common”. The intersection of A and B, denoted by A ∩ B, is the set of all things which are members of both A and B. If A ∩ B = ∅, then A and B are said to be disjoint.
Examples:

 {1, 2} ∩ {red, white} = ∅.
 {1, 2, green} ∩ {red, white, green} = {green}.
 {1, 2} ∩ {1, 2} = {1, 2}.
Some basic properties of intersections:

 A ∩ B = B ∩ A.
 A ∩ (B ∩ C) = (A ∩ B) ∩ C.
 A ∩ B ⊆ A.
 A ∩ A = A.
 A ∩ ∅ = ∅.
 A ⊆ B if and only if A ∩ B = A.
[edit]Complements
Two sets can also be “subtracted”. The relative complement of A in B (also called the set theoretic difference of B and A), denoted by B \A, (or B −A) is the set of all elements which are members of B, but not members of A. Note that it is valid to “subtract” members of a set that are not in the set, such as removing the element green from the set {1, 2, 3}; doing so has no effect.
In certain settings all sets under discussion are considered to be subsets of a given universal set U. In such cases, U \ A is called the absolute complement or simply complement of A, and is denoted by A′.
Examples:

 {1, 2} \ {red, white} = {1, 2}.
 {1, 2, green} \ {red, white, green} = {1, 2}.
 {1, 2} \ {1, 2} = ∅.
 {1, 2, 3, 4} \ {1, 3} = {2, 4}.
 If U is the set of integers, E is the set of even integers, and O is the set of odd integers, then the complement of E in U is O, or equivalently, E′ = O.
Some basic properties of complements:

 A ∪ A′ = U.
 A ∩ A′ = ∅.
 (A′)′ = A.
 A \ A = ∅.
 U′ = ∅ and ∅′ = U.
 A \ B = A ∩ B′.
Cartesian product
A new set can be constructed by associating every element of one set with every element of another set. The Cartesian product of two sets A and B, denoted by A × B is the set of all ordered pairs (a, b) such that a is a member of A and b is a member of B.
Examples:
 {1, 2} × {red, white} = {(1, red), (1, white), (2, red), (2, white)}.
 {1, 2, green} × {red, white, green} = {(1, red), (1, white), (1, green), (2, red), (2, white), (2, green), (green, red), (green, white), (green, green)}.
 {1, 2} × {1, 2} = {(1, 1), (1, 2), (2, 1), (2, 2)}.
Some basic properties of cartesian products:
 A × ∅ = ∅.
 A × (B ∪ C) = (A × B) ∪ (A × C).
 (A ∪ B) × C = (A × C) ∪ (B × C).
Let A and B be finite sets. Then
  A × B  =  B × A  =  A  ×  B .