Number line

In mathematics it is accepted to represent numbers as a number line. We will consider transformation of number ray to the number line.

Reverse symmetry allows to get numbers less unit. As a point of reverse symmetry is unit, this symmetry does not depend on units of measurement. Reverse symmetry reflects relativity of concepts "greater than unit" and "less than unit" at comparison of two numbers. In case of comparison of two numbers without fail it is needed to accept one of these numbers as unit of measurement.

After introduction of unit of measurement we get the absolute system of coordinates for any unit of measurement. Unit of measurement on a picture is represented in the traditionally accepted variant - with imposition on the area of reverse numbers. At imposition of mirror symmetry the point of that is a zero, we enter negative numbers and get the relative system of coordinates. All enumerated transformations are represented on a picture below, where the sign of endlessness is mark any number.

Number line. Number ray. Mathematics For Blondes.
Expl for blondes: Farther we will consider relativity of concept "Any number".


Multiplication chart

Multiplication chart. Printable multiplication table. Multiplication tables chart 1 to 10. Mathematics for blondes.

Multiplication chart, printable multiplication table, multiplication tables chart 1 to 10 for you from mathematics for blondes.

Look similarly The multiplication table 1 to 20.


Relativity is in mathematics

All distinctions between two numbers or two units of measurements come to light only at comparison of two numbers or two units of measurements. All results of comparison are relative, as depend on what from two elements takes up basis at comparison. Relativity of results of comparison is represented different kind by symmetries. If up basis of symmetry a point takes "zero", then mirror symmetry ensues. If up basis of symmetry a point takes "unit" - reverse symmetry ensues. For units of measurements of corners reverse symmetry is transformed in perpendicular symmetry that is possessed by the values of trigonometric functions.

All distinctions between two numbers or two units come to light only at comparison of two numbers or two units. All results Comparison of two any numbers is not possible without the presence of the general founding unit comes forward as that. For the location of any numbers in order of growth in modern mathematics as unit of numbers the number systems are used: binary, ternary, octal, decimal, sexadecimal et al. Comparing of two numbers to the different grounds is not possible without bringing them over to the general founding.

Comparison of two numbers at different units of measurements becomes possible at the use of the third unit of measurement - one of the number systems, for example, decimal.

Result of comparison of two numbers is described by concepts "greater than" and "less than". Relativity of comparison of numbers is expressed in that the result of comparison depends on that, what number takes up basis at comparison. For example, if to compare numbers 2 and 3, we will get two results:

2 less than 3
3 greater than 2

On the first place it is accepted to write down a number that takes up basis at comparison, on the second is a that number it is compared to that. The results of comparison possess property of mirror symmetry - at the change of founding a result changes on opposite. The point of mirror symmetry is equality of two compared numbers. The results of comparison of two numbers are analogical to the relative system of coordinates:

less than - equal - greater than
minus - zero - plus

Comparison of two units of measurements is possible at presence of general point "zero". The result of comparison of two different units of measurements can be a conclusion about perpendicularity or parallelism of these units of measurements. Parallelism or perpendicularity of one unit of measurement in relation to other is concepts relative.

Expl for blondes: we will examine farther, as well as where a Number line appeared from.

Some concepts of mathematics are continuation

A point is this reserved space with the radius of curvature equal to the zero (Expl for blondes: I do not understand clearly, that means this phrase. But I know exactly, that she is correct and very useful for us, when we will begin to examine mathematical principles of teleportation. To ride on an own car even prestige - it not so already prestige. In fact you however will escape farther than this planet. And here with you, even with blondes, the same, that happened to the dinosaurs will happen sooner or later - nature you will kill. Where will you escape from a submarine boat, even if this boat measuring with a planet?). Any space consists of endless amount of points. Through any point of space it is possible to conduct an endless amount mutually perpendicular lines. All points of space possess properties of both zero and unit, that allows without difficulty and arbitrarily to impose any relative system of coordinates and apply any type of symmetry in any point of space. In any point of space equality is executed: a zero is equal to unit. Equalization of point 0 = 1. Properties of zero and unit for one point of space can not show up simultaneously in one system of coordinates.

A line is this open-space with the radius of curvature equal to unit divided by a zero, consisting of separate points.

In mathematics it is necessary to distinguish the next types of corners : corner of scale, trigonometric corner, corner of turn.

Corner of scale is a corner scope from 0 to 90 degrees. The corner of scale can equal a zero, but 90 degrees can not equal. This corner reflects quantitative changes within the limits of one unit of measurement. Any changes of corner of scale can not cause the quality change of unit of measurement.

A trigonometric corner is a corner scope from 0 to 90 degrees. A trigonometric corner can equal both a zero and 90 degrees. This corner reflects dependences between units of measurements (project properties of space) and condition of quality changes of units of measurements. Dependence of quantitative changes of units of measurements on a trigonometric corner is expressed by trigonometric functions. The quality changes of units take place at the values of trigonometric functions equal to the zero and unit divided by a zero.

A corner of rotation is a corner that can have any values. In a range from 0 to 90 degrees the corner of rotation numeral can coincide with a trigonometric corner or corner of scale. The corner of rotation reflects the circular moving without the change of quantitative or quality descriptions of unit.

A direct corner differs from all other corners that the mutual projection of two intersecting lines is a point. For all other values of corner the projection of one line on other is a line. At coal equal to the zero, lines coincide. Mathematical unit of corners is a corner equal 45 degrees. This unit of corners submits to the rules of the binary number system.

Expl for blondes: Thereon the set of clever mathematical words is closed and we pass to consideration of mathematical mechanism - that, as and why works in mathematics. We will begin our excursion with relativity in mathematics.