**Magician** ,

** Exergy & Entropy. ** and great delusions.....and whatever great words...

I love my delusion about Patterns and Order, they give me enough info to

take the right decision most of the times when i bet . Can be done flat bet

or with possitve progression (chart s flat bet).

This quote shows that order is part of math.

But there is much more about this ...math/patterns/order....

search yourself.

Quote:

**

Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary.

Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.g. "2 is less than 3", "10 is greater than 5", or "Does Tom have fewer cookies than Sally?". This intuitive concept can be extended to orders on other sets of numbers, such as the integers and the reals. The idea of being greater than or less than another number is one of the basic intuitions of number systems (compare with numeral systems) in general (although one usually is also interested in the actual difference of two numbers, which is not given by the order). Other familiar examples of orderings are the alphabetical order of words in a dictionary and the genealogical property of lineal descent within a group of people.

The notion of order is very general, extending beyond contexts that have an immediate, intuitive feel of sequence or relative quantity. In other contexts orders may capture notions of containment or specialization. Abstractly, this type of order amounts to the subset relation, e.g., "Pediatricians are physicians," and "Circles are merely special-case ellipses."

Some orders, like "less-than" on the natural numbers and alphabetical order on words, have a special property: each element can be compared to any other element, i.e. it is smaller (earlier) than, larger (later) than, or identical to. However, many other orders do not. Consider for example the subset order on a collection of sets: though the set of birds and the set of dogs are both subsets of the set of animals, neither the birds nor the dogs constitutes a subset of the other. Those orders like the "subset-of" relation for which there exist incomparable elements are called partial orders; orders for which every pair of elements is comparable are total orders.

Order theory captures the intuition of orders that arises from such examples in a general setting. This is achieved by specifying properties that a relation ≤ must have to be a mathematical order. This more abstract approach makes much sense, because one can derive numerous theorems in the general setting, without focusing on the details of any particular order. These insights can then be readily transferred to many less abstract applications.

Driven by the wide practical usage of orders, numerous special kinds of ordered sets have been defined, some of which have grown into mathematical fields of their own. In addition, order theory does not restrict itself to the various classes of ordering relations, but also considers appropriate functions between them. A simple example of an order theoretic property for functions comes from analysis where monotone functions are frequently found.

Partially ordered sets[edit]

Orders are special binary relations. Suppose that P is a set and that ≤ is a relation on P. Then ≤ is a partial order if it is reflexive, antisymmetric, and transitive, i.e., for all a, b and c in P, we have that:

a ≤ a (reflexivity)

if a ≤ b and b ≤ a then a = b (antisymmetry)

if a ≤ b and b ≤ c then a ≤ c (transitivity).

A set with a partial order on it is called a partially ordered set, poset, or just an ordered set if the intended meaning is clear. By checking these properties, one immediately sees that the well-known orders on natural numbers, integers, rational numbers and reals are all orders in the above sense. However, they have the additional property of being total, i.e., for all a and b in P, we have that:

a ≤ b or b ≤ a (connex property).

These orders can also be called linear orders or chains. While many classical orders are linear, the subset order on sets provides an example where this is not the case. Another example is given by the divisibility (or "is-a-factor-of") relation "|". For two natural numbers n and m, we write n|m if n divides m without remainder. One easily sees that this yields a partial order. The identity relation = on any set is also a partial order in which every two distinct elements are incomparable. It is also the only relation that is both a partial order and an equivalence relation. Many advanced properties of posets are interesting mainly for non-linear orders.

And.....so on............ ***