Some concepts of mathematics

Expl for blondes: "Some concepts of mathematics" are my crib on your own, darling. Deciding some mathematical question, I often had to remember the own non-standard decisions of other questions. What is long not to dig in the memory, I collected all most important moments at the beginning of cycle of reasons of "Bases of mathematics". Some articles from this cycle will bring us over to the conclusions that is already writtenin here.

Equal sign reflects dependence of causality in the surrounding world. (Expl for blondes: is the example of application of the first basic axiom of mathematics.) If 2 х 2 = 4, it not nearly means that 4 = 2 х 2. There is an endless great number of decisions resulting in an exactly such result - four. 2 х 2 - only one of these decisions.

In mathematics there are three basic equalities:

0 = 0
1 = 1
0 = 1

All physical laws and mathematical equalizations are taken to one of these equalities. (Expl for blondes: do you think why I so easily succeeded to find the decision of the undecided equalizations (in Rassian)? Because I beforehand know an answer - the decision of any mathematical equalization is taken to one of these equalities. If know a problem specification and right answer, decision to find much simpler. By the way, here one of remarks of physicists, about that I wrote in the article "Zero is equal to unit": "Sum of energy of substance and gravitational energy is saved, but this law of maintenance is unusual: this sum is equal to ZERO"!. Most strikes me circumstance that physicists result in mathematics, as old jade! But it must be quite the reverse - it mathematicians must explain to the physicists: that, as and why works in this world. Physics is an experimental base of mathematics. If physicists will find some exceptions from mathematical rules, means to the mathematicians it will be needed to correct mathematics.)

In mathematics it is possible to distinguish such basic elements: zero, unit, any number and unit of measurement.

Numbers reflect quantitative description anything. Any number is equal to any number - this property of numbers allows to distinguish them in the special group that it is accepted to designate a word "number". All separately taken numbers possess identical mathematical properties. (Expl for blondes: not surprised, most bad dream of any mathematician (all numbers are equal) is cruel mathematical reality. Do not be afraid, I do not gather to take from mathematicians their favourite toy that are numbers. I simply want to say an obvious thing: all of you know many most different toys (and child, and adults), but all unites them one property - it is possible to play by them.)

Any number is the positive real number more unit. If to one any number to add other any number the first number will increase. Just any number will increase at multiplying of him by other any number. If from any number to subtract other any number, the first number will diminish. If to divide one any number into other any number, the first number will diminish.

Unit is a number, but is not any number, as at multiplying and dividing by unit any number remains unchanging. Unit is a neutral element at an increase and division.

Geometrically any number is represented by a point. All numbers form a numerical ray with beginning in a point "unit". A numerical ray does not have an end. Any number can be designated by a sign "infinity", as any number can be how pleasingly great.

Units of measurement reflect quality description anything. Any unit of measurement is equal to any unit of measurement. All units of measurement possess identical mathematical properties. (Expl for blondes: In mathematics units of measurement symmetric to the numbers, will remember an axiom about symmetry.) For numbers universal units of measurement are the number systems: binary, decimal, sexadecimal to and other. (Expl for blondes: I think, for mathematicians it will be the real discovery. I in any way can not get used to that any writtenin number has a tail of unit of measurement is "abstract unit".)

Geometrically any unit of measurement is represented by a segment (by two points): point "zero" is this beginning of unit of measurement, point "unit" is an end of unit of measurement.

Zero is not a number, as at addition of zero to any number and deduction of zero from any number this number remains unchanging. (Expl for blondes: It there is that simple and elegant decision of problem with zero about that I talked before. I agree, it is another act of mocking above mathematical sacred objects. But, there be nothing to be done - beauty of mathematics requires victims. you only present, how many energy and paper we will economize, if we will not in every example on a division write a "denominator does not equal a zero". Environmentalists will be happy here!) Zero is a neutral element at addition and deduction. Zero is beginning of the absolute system of coordinates. In the relative system of coordinates zero is the point of mirror symmetry.

In a point "unit" takes place connection of unit of measurement with any numbers. Unit is the point of reverse symmetry in the absolute and relative systems of coordinates.

Expl for blondes: It is a yet not end. Tomorrow we will continue to examine some mathematical concepts.


Basic axioms of mathematics

Mathematics is laws there is the surrounding world on that. The laws of mathematics are identical for any universes with any amount of measuring.

Mathematics - it governed without exceptions. If an exception appears in a mathematical rule - this rule must be changed. This statement is the universal formula of the scientific discovery in mathematics.

Mathematics is abstraction. The abstract of mathematics consists in that the laws of mathematics operate always and everywhere identically.

Mathematics is the closed system. If a correct mathematical result is got, then there is an infinite amount of ways resulting in an exactly such result.

Mathematics is symmetry. Absolute symmetry in mathematics is a limit of development of mathematics as sciences.

Mathematics is relativity. Positive and negative numbers do not exist in the wild. Positive and negative numbers are this reflection of our personal opinion in mathematics. A negative number is a sign of the relative system of coordinates, position of that depends exceptionally on our choice of her center. A the same point can have different signs and different numerical values in the different relative systems of coordinates.

Mathematics is basis of commonunication and mutual understanding of reasonable creatures from different civilizations. Geometry translators does not need. Mathematics is closed wherein human logic begins.

Expl for blondes: in more detail we will consider each of these axioms a bit later, and while we will continue an acquaintance with mathematics and will look at some concepts that will be used in future.


Bases of mathematics

Bases of mathematics are a cycle of my reasons. Main task of "Bases of mathematics" - to complement mathematics the absent fragments of mathematical knowledge and set intercommunications between some copy-book maxims already known to us.

Most useful innovations in mathematics will be units of measurement and divizion by zero. Clear that to explain it it will be not simply. For understanding will be thoroughly to understand some generally accepted mathematical concepts to set that there is a true in them, and that is lie.

Why are units of measurement needed in mathematics? Here imagine such situation. Does a child go near you, hands to you an object asks: "That will happen, if to drop this object?" Using principles of modern mathematics, you need to take the list of all great numbers of objects to find, to what great number from existing this object belongs. If this great number of the broken up objects, then this concrete object will be broken up. If this great number of jumpings up objects, then this object will jump up. In the existent lists of great numbers of objects you will have to be long and boring dug, before you will be able to find an answer for a question.

Is it possible to decide a problem simpler? It is possible. If by sight to determine material out of that an object is made and to know properties of this material - then no problems. A glass object will be broken up, a rubber ball will jump up, a ferrous ring will do "drin" and jelly will do "tuff".

Just in mathematics there is business with units of measurement. If you know mathematical properties of unit of measurement, you will say without effort, that can be expected and what it is impossible from a that physical parameter that this unit of measurement belongs to.

Introduction to mathematics of units of measurement as a mathematical element equivalent to the numbers, allows to determine mathematical methods many fundamental properties of the surrounding world.

If you think that as a result of such innovations of mathematician will become yet tangled, you wrong. Mathematics will be simpler, more slender, clearer. Look at the basic axioms of mathematics.