PEDREIRA, Sinvaldo Martins [1] [2]

PEDREIRA, Sinvaldo Martins. **The value of number**s. Multidisciplinary Core scientific journal of knowledge. Year 1, vol. 8. pp. 5-16, September 2016. ISSN. 2448-0959

**SUMMARY**

This work aims to show a new vision about what are the numbers and their representativeness with the reality, through a systematic and rational, objective to characterize the equacionais steps in a clear and succinct, correcting arithmetic anomalies caused by misunderstandings of interpretation of how to behave, numeric terms that are commonly used in mathematical context and the different units generally factorials without worrying about the individual uniqueness that each component has.

Throughout human history man has followed form at the rules imposed by the current system and when it is at a crossroads invents amazing, rules high degree of creativity, but of little efficacy since their solutions lie in the imaginary plane of reality, purely based on rules, not on rational principles.

**PREFACE**

The numbers are designed to quantify something, be it by proportion or measure (length, area, volume, time, weight, etc.).

Worldwide was the use of numeric symbols Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Where:

The 0 symb__o__l identifies the number zero.

The 1 symbo__l__ identifies the number one.

The symbo__l __2 identifies the number two.

The 3 symbo__l__ identifies the number three.

And there on …

It was also agreed that they would be grouped together in units, tens, hundreds, etc. …

Ex:

123:123.

One hundred, two dozen and three units.

Possession of a mathematical precept people have learned to count things, sum them and subtracts them.

* Note. With the advent of subtracting negative numbers came into existence, identified by the sign (-) before the number.

Ex:

-1 = least one

-15 = least 15.

And the numbers were ordered as follows:

(… -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. …)

Later learned-if the multiply and divide things, thus, the four fundamental equations.

Addition (+).

Subtraction (-).

Multiplication (x).

Division (/).

Addition: 5 + 6 = 11 12 + 3 = 15 4 + 8 = 12 13 + 18 = 31

Subtraction: 8-3 = 5:15-4 = 11 25-7 = 18 20-6 = 14

Multiplication: 5 x 7 = 35 2 x 4 = 8 6 x 9 = 54 12 x 3 = 36

Division: 8/2 = 4 40/5 = 8 70/10 = 7 55/11 = 5

But noticed some peculiarities when using negative numbers (-), not only in subtractions, but several:

** 1st speciality:**

Subtraction: -4 + 3 = -7 + -1 = -15 + +1 8 8 = -2 + 1 -7 = -1

Addition: +8 +6 = +1 +2 = +14 -5 = -10 -12 -5 +3 -13 = -25

Multiplication: +3 x 7 = +21 +3 -7 = -3 x -21 x 7 = -3 -7 = +21 x -21

Division: +10/+5 = +2 +10 = -10/ -2 -5/+5 = -10/ -2 -5 = +2

When a number is multiplied or divided the rule is as follows:

(Plus more) + + = + (positive)

(More with less) +-=-(negative)

(More)-+ =-(negative)

(Less with less)–= + (positive)

** second peculiarity**

** Empowerment and nth root.**

+5² = 25 -5² = +25 + 5³ = +125 -5³ = -125

+3² = 9 -3² = +9 +3³ = +27 -3³ = -27

Following the rule.

+5 x +5 x -5 = -5 +25 = +25 x +5 x +5 = +5 + -5 x -5 x 125-5 =-125

+3 x +3 x -3 = -3 +9 = +9 x +3 x +3 +3 x -3 -3 x +27 = -3 = -27

Corresponding:

__– -25 -5-1 0 1 5 25 125 125__

** 5² 5³**

Group

+5 * = 1, 5, 25, 125, ordered …

__. .__

__ – -25 -5-1 0 1 5 25 125 125__

** -5³ ? -5¹ ? -5º -5² **

Group

* -5 = 1, -5, 25, -125, random …

__. .__

__-27 -9 -3 -1 0 1 3 9 27__** 3º 3¹ 3² 3³**

Group

+3 * = 1, 3, 9, 27, … ordained

__. .__

__-27 -9 -3 -1 0 1 3 9 27__** **

** **** -3³ ? -3¹ ? 3º -3² **

Group

-3 * = 1, .9 -3, -27, random …

__. .__

__3rd peculiarity__

2 + 0 = 2

2-0 = 2

2 x 0 = 0

2/0 = there is no satisfactory answer (unknown).

__. .__

__The value of the numbers__

So far we have seen that the numbers appeared to quantify things, being created for the four fundamental equations:

Addition, subtraction, multiplication, and Division.

We also saw that the numbers are represented by two separate signals (+) positive and (-) negative, also being planned in this way:

__… -10- -8 -6 -5 -4 -7 9 -3 -2 -1 +1 +2 +3 +4 +5 0 +6 +7 +8 +9 + 10.__

** How are used.**

By working with calculations treat the terms generically, are positive (+) or negative (-), without worry about what each numeric term represents.

Ex:

+ 50-20 + 50 + 30 = 30 = 80

-50-30 =-80-50 + 30 = -20

50 +-( -30) = + 80 + 50 + ( -30) = +20

+ 50 + (+30) = + 80-50-( -30) = -20

-50 + (+30) = -20-50-(+30) =-80

5 x 3 = 15 5 x -3 = -15

-5 x 3 = -5 x -3 = -15 +15

10/2 = + 5 10/ -2 = -5

-10/2 = -10/ -5 -2 = +5

All calculations are correct according to the rules in force.

**Are they correct even?**

__The root of the matter.__

For a better view of the matter, let's call the numbers:

Positive (+) of "Concretes".

Why concretes (+)?

Because they represent something, anything.

Negative (-) of "Abstract".

Why abstract (-)?

Because they reflect the lack of something, a pending.

__IMPORTANT NOTE:__

It was agreed the use of the sign (+) to indicate that a number is positive as to indicate an addition (sum), but this is a misconception, since the arithmetic provided a positive number indicates a numerical quality, while an addition indicates an equation between terms i.e. an action between numerical factors.

It was agreed the use of the sign (-) to indicate that a number is negative as to indicate a subtraction (difference), but this is a misconception, since the arithmetic provided a negative number indicates a numerical quality, while a minus sign indicates a difference between equation terms i.e. an action between numerical factors.

To resolve the problem:

We will continue using the plus sign (+) to identify that the number is positive and the sign (-) to identify that the number is negative.

The addition will be represented by the letter (U).

The subtraction will be represented by the letter (H).

Ex:

+5__ U + +8 U + 3 =____ +__7 = 7 +4 = 8 +14__ __U + +12

+3 __U__ -9 = -6 +5 __U __ -1 = +4 – 8 __U __ -9 = -17

+__9__ H +4 +8 -5 +5__ __= H = -7 -8 = +__1__ +13 H

-4 __H__ -2 = -2 -2 __H__ -4 = +2 +1 __H __-5 = +6

__Paradox.__

**Multiplication.**

**+5 x +4 = +20 will be?**

+5 x +4 = o**r**anges oranges? (Irrational) "things do not multiply things".

**+5 x -4 = -20 will be?**

+5 x -4 = o**r**anges oranges? (Irrational) "things don't multiply backlogs".

**-5 x +4 = -20 will be?**

-5 x +4 = **o**ranges oranges? (Irrational) "backlogs not multiply things".

**-5 x -4 = +20 will be?**

-5 x -4 = **o**ranges oranges? (Irrational) "backlogs don't multiply backlogs".

**Division.**

**+10/+2 = +5 will be?**

+10/+2 = s**to**nes stones? (Irrational) "things are not divided by things".

**+10/ -2 = -5 will be?**

+10/ -2 =** s**tones stones? (Irrational) "things are not divided by backlogs".

**-10/+2 = -5 will be?**

-10/+2 = **st**ones stones? (Irrational) "backlogs are not divided by things".

**-1**0**/** **-2 = -5 will be?**

-10/ -2 **= **stones stones? (Irrational) "backlogs are not divided by backlogs".

**How to solve the problem?**

To solve the problem we need a value-neutral (n), not (+) or (-) concrete and abstract, a term that represents the geometric reason by which we must multiply or divide things up or loose ends.

For a better view, we use neutral and call numbers:

(° n). Geometric (x) or (/). "Represent the geometric reason by which a number should be multiplied or divided, not having concrete or abstract value, being so neutral".

Ex:

**Multiplication.**

**º 8 x +5 = + 40 will be?**

º 8 x +5 = + 40 oranges oranges (rational).

**º 8 x -5 =-40 will be?**

º 8 x -5 =-40 oranges oranges (rational).

**Division.**

**+10% = +5 2 will be?**

+10% = 2 stones +5 stones (rational).

**-10% = -5 2 will be?**

-10% = 2 stones -5 stones (rational).

__. .__

__How they should be used__

As has been seen, the terms of a computation should not be used in a generic way, only having value (+) or (-), we should use the terms according to their specific representation, for specific cases.

We will use the symbols:

(+) positive term (concrete)

(-) negative term (abstract)

(n) neutral (geometric) term used in multiplication (x) or (/) Division.

** The numbers have value defined thus planned:**

**x**:

No. 6 (x)

# 5

# 4

# 3

° 2

# 1

__(-) …-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6… (+)__

# 1

# 2

# 3

# 4

# 5

No. 6 (/)

:

**/**

On the shaft of the "Ordered" contained only the numbers (n) geometric (x) at the top and multiplication (/) Division at the bottom.

On the "Abscissas" contained the numbers (-) negative on the left and positive (+) on the right side.

__Rules.__

Numbers (+) positive and (-) negative can add, subtract, be multiplied or divided.

* Never multiply or divide.

Numbers (n) geometric (x) or (/) multiply divide numbers (+) positive or (-) abstract.

* Never being multiplied or divided by numbers (+) or (-).

Ex:

+5 U +10 U -6 +5 +5 = -1 -8 = +2 -6 = U

-3 U -4 = -7

º +30 º 5 x +6 = 5 -3 = -8 x -15 x° 5 = does not satisfy the rule.

-30% = -5 +12/6° = +3° 21/4 -7 = does not satisfy the rule.

__Long-term potentiation__

+5² = 25 -5² = -25 + 5³ = +125 -5³ = -125

+3² = 9 -3² = -9 +3³ = +27 -3³ = -27

**Following the rule.**

º +25 º 5 x +5 = 5 x -5 = -25 # 5 x (5 x +5) = + 125

No. 5 x (5 x -5) =-125

º 3 x +3 = +9 # 3 x -3 = -9 # 3 x (3 x +3) = +27

º 3 x (3 x -3) = -27

Corresponding:

__– -25 -5-1 0 1 5 25 125 125__

** 5° 5¹ 5² 5³ **

Group

+5 * = 1, 5, 25, 125, … Ordained

__. .__

__– -5- -25-1 0 1 5 25 125 12__**5**

**5³ -5² -5¹ -5º **

Group

* -5 = -1, -5, -25,-125, … Ordained

__. .__

__-27 -9 -3 -1 0 1 3 9 27__** **

** 3º 3¹ 3² 3³**

Group

* +3 = +1, +3, +9, +27, … ordained

__. .__

__-27 -9 -3 -1 0 1 3 9 27__

**-3³ -3² -3¹ -3º **

Group

-3 * =-1.0-3.0-9.0-27, … Ordained

__. .__

__Case Zero__

The number (0) zero is a term insubstantial, does not have any value, represents the empty because it is null, not to be confused with null.

The term (0) zero has no value (+) positive or (-) negative and cannot be added or subtracted, multiplied or divided and nor is (n) neutral doesn't (x) multiplies or (/) divides any other number.

(0) zero serves solely as a result of an addition or subtraction where the terms cancel each other out.

Ex:

+4 -4 = 0 +3 = 0 +5 -8 + -10 -25 = 0 35

+2 +0 = does not exist "(0) zero is null"

+2 -0 = does not exist "(0) zero is null"

# 2 x 0 = does not exist "(0) zero is null"

0% 2 = does not exist "(0) zero is null"

__. .__

__Exceptional cases__

There are conceptual cases due to the fact they represent measures and not things, can be represented by numbers (+), negative (-) and (n) geometric.

**1st Case. **** Time**: you can either move the axis of Abscissas when subtracts or add time as multiplied and divided.

Abscissas with sorted, when expressed.

**2nd case. **** Dimensi**on: both can move in the abscissa axis, when you subtract or add measures such as multiplied and divided.

Abscissas with sorted; When expressed space.

Abscissas and ordinates with depth; When expressed.

**third case. **__Mass____:__ both can move the axis of Abscissas, when weight can be added exemplifies, subtracted, as multiplied and divided.

**4th case. **__Physical conc____e__pts: concepts can merge

ex: speed, density, strength, etc. .. passing of systemic form, by plotting, Abscissas and depth.

**Final considerations **

In possession of a new mathematical reality, open various possibilities to solve problems in the most diverse fields of science, technology and rationality, as the equations will be seen more broadly, because their parties have specific meaning and own, a geometric, three-dimensional universe if formed more visible in the eyes of those who pay attention around the limit is infinity.

[1] Mathematician, a civil servant of the city of São Paulo. Email: [email protected]

[2] This work it is a result of research for developing a thesis on behavior between positive numbers and negative, giving support to the author recreate a parallel theory.

Anderson de Souza Merighi 2/24/2017 at 5:21 pm

Lord Sinvaldo, you present the result of a potentiation of a negative number high to the exponent pair as a negative number (-5² = -25). I did not understand how you got to that result.

Thank you!

answer

Sinvaldo Martins Pedreira 03/01/2017 at 7:40 pm

Hello, Anderson, the positive numbers (+), are those that represent something that exists, something concrete.

The negative numbers (-), are those that represent debts, pending or is the lack of something.

Geometric ratios (ºn) are numbers that represent how much something must be multiplied or divided, not having positive (+) or negative (-), being neutral (ºn).

Hence a squared number is the result of a geometric ratio multiplied by a number of the same degree, ie, (n) x (+) = (+) and (n) x (-) = (-)

So 5² = º5 x +5 = +25 and -5² = º5 x -5 = -25

I hope I have healed the doubt.

Carlos Eduardo Ribeiro da Costa 03/23/2017 at 5:48 pm

Mr. Sinvaldo, good afternoon!

I really liked the article and didactics used (reminded me by a college professor when he said “orange multiplies orange”) and I even understood the question of potentiation with high negative numbers by even numbers, it is not logical to have an empty result, since I understand that If we have two empty holes and we raise to the square, we will have four empty holes and not four holes full.

But you have to agree that the mathematics we have known has been tested for centuries, though nothing prevents it from being wrong, and there are those who contest Einstein’s calculations, but what you suggest is a revolution in the way of calculating and we would have to review everything, From the beginning … it is evident that this thesis must have been tested and also proven through a bank of experts sympathetic to it.

I ask: You have proof of this thesis in practice and you already have an idea of the revolution caused in mathematics if this thesis is correct?

answer

Sinvaldo Martins Pedreira 3/27/2017 at 6:58 pm

Good afternoon, Mr. Carlos Eduardo.

Well, first let’s put order in the house.

Any and every equation is formed by two classes of numbers, which we will call Base and components,

Base = the sum of the components and

Component = difference from Base to one or more Components

Ex.

We will use the symbol U to identify sum and the symbol D to identify difference

8 = 5 or 3 -> 8 D 5 = 3 -> 8 D 3 = 5 see that even if we change the terms of side we do not change the signal because base and components are immutable, 8 D 3 = 5 -> 3 = 8 D Referring to Fig.

Another example

5 = 7 U -2 -> 5 D 7 = -2 -> 5 D -2 = 7

second degree equation.

(A U B) ² = C² …. C2 = ºC x C we then deduce that

° C x (A U B) = C 2

EX.

(4 U B) = 49 -> 7 x 4 U 7 x B = 49 -> 28 U 7B = 49 -> 7B = 49 D 28 -> 7B = 21 -> B = 21/7 -> B = 3

Other ex

(A D 8) ² = 9 -> 3 x A D 3 x 8 = 9 -> 3A D 24 = 9 -> 3A = 9 U 24 -> 3A = 33 -> A = 33/3 -> A = 11

You see, the rules and equations are exact and simple, making Bhaskara wrong.

Use the rule of base and components as you wish and you will see for yourself how much revolution I do not know, but it is fact.