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. More interesting things on the page "New Math".