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Showing posts with label deduction. Show all posts
Showing posts with label deduction. Show all posts

3.18.2011

About symmetry of mathematical actions

About symmetry of mathematical actions - is my first official publication. To all appearances, my flaming speech under the name "Mathematics forever!" remained unnoticed. It is clear. Reading a like, I would say that a next idiot rushed about on all Internet with the ridiculous idea. But... All, that is here written, I write exceptionally for you and publish here in an only copy, unlike other authors of raving ideas. With my article about symmetry of mathematical actions you are first can become familiar right here and now. I am herein anything interesting or no - decide. In brackets I will give some comments (specially for you) that in the printed variant of the article are absent.

Annotation: Rules of symmetry of mathematical actions allow to apply a commutative law to all mathematical actions: to addition, deduction, multiplication and division. (An annotation is this obligatory condition for the publication of the article. Such are rules of the bureaucratic playing science)

Changes in the surrounding world are expressed by mathematical actions. Quantitative changes are expressed by addition and deduction. Quality changes are expressed by an increase and division. No quantitative changes can cause the change of quality.

Quantitative changes reflect the change of amount of the separately taken unit. Addition and deduction are symmetric mathematical actions reflecting the quantitative changes of any unit. Addition and deduction are mirror symmetric relatively neutral element are points zero.

An increase and division similarly are symmetric mathematical actions reflecting the quality changes of units. An increase and division are back symmetric relatively neutral element are points one.

Rules of symmetry of mathematical actions:

1. Any mathematical action is begun with a neutral element.

2. A sign of mathematical action is the inalienable attribute of number before that he stands.
(This fragment is distinguished by me by fat text specially for you)

Application of these rules allows to apply a commutative law to all mathematical actions reflecting quality or quantitative changes.

0 + 3 + 7 + 4 = 0 + 7 + 3 + 4 = 14

0 – 3 – 7 – 4 = 0 – 7 – 3 – 4 = –14

0 + 3 – 7 – 4 = 0 – 7 + 3 – 4 = –8

1 х 3 х 7 х 4 = 1 х 7 х 3 х 4 = 84

1 : 3 : 7 : 4 = 1 : 7 : 3 : 4 = 1/84

1 х 3 : 7 : 4 = 1 : 7 х 3 : 4 = 3/28

A commutative law can not be used in the cases of the mixed implementation of mathematical actions reflecting quality and quantitative changes in one mathematical expression.

The change of the mathematical operating on symmetric gives a symmetric result, here the point of symmetry is a neutral element. Application of commutative law does not influence on a result.

0 – 3 – 7 – 4 = 0 – 7 – 3 – 4 = –14

0 + 3 + 7 + 4 = 0 + 7 + 3 + 4 = 14

0 – 3 + 7 + 4 = 0 + 7 – 3 + 4 = 8

1 : 3 : 7 : 4 = 1 : 7 : 3 : 4 = 1/84

1 х 3 х 7 х 4 = 1 х 7 х 3 х 4 = 84

1 : 3 х 7 х 4 = 1 х 7 : 3 х 4 = 28/3

Running the numbers in the mathematical operating on symmetric relatively neutral element of number gives a symmetric result.

0 + (–3) + (–7) + (–4) = 0 + (–7) + (–3) + (–4) = –14

0 – (–3) – (–7) – (–4) = 0 – (–7) – (–3) – (–4) = 14

0 + (–3) – (–7) – (–4) = 0 – (–7) + (–3) – (–4) = 8

1 х 1/3 х 1/7 х 1/4 = 1 х 1/7 х 1/3 х 1/4 = 1/84

1 : 1/3 : 1/7 : 1/4 = 1 : 1/7 : 1/3 : 1/4 = 84

1 х 1/3 : 1/7 : 4 = 1 : 1/7 х 1/3 : 1/4 = 28/3

Simultaneous change of the mathematical operating on symmetric and running the numbers on symmetric relatively neutral element of number abandons a result without changes.

0 – (–3) – (–7) – (–4) = 0 – (–7) – (–3) – (–4) = 14

0 + (–3) + (–7) + (–4) = 0 + (–7) + (–3) + (–4) = –14

0 – (–3) + (–7) + (–4) = 0 + (–7) – (–3) + (–4) = –8

1 : 1/3 : 1/7 : 1/4 = 1 : 1/7 : 1/3 : 1/4 = 84

1 х 1/3 х 1/7 х 1/4 = 1 х 1/7 х 1/3 х 1/4 = 1/84

1 : 1/3 х 1/7 х 4 = 1 х 1/7 : 1/3 х 1/4 = 3/28

The neutral elements of mathematical actions it is not accepted to write at the decision of mathematical problems and examples, as they do not influence on a result. Before application of commutative law introduction of neutral elements allows correctly to apply a commutative law.

All of it is written, certainly, not for blondes, and for mathematicians. In the future we yet not once will call to this article. And while... you know any more mathematician about symmetry of mathematical actions.

8.23.2010

Enter numbers the difference of numbers zero and twenty

"Enter numbers the difference of numbers 0 (zero) and 20 (twenty)" - a similar task very often meets in the Internet. Interesting that I do not know exactly, how her it is correct to decide. Omniscient Wikipedia reports bashfully, that a difference of numbers is a result of deduction of two numbers. But here, as correct to execute the action of deduction, this collection of wisdom holds back. In fact two variants of decision of this task are possible:

1. From the first number to subtract second 0 - 20 = - 20 (to take away zero twenty evened minus twenty)

2. From a greater number to subtract less 20 - 0 = 20 (twenty to take away zero evened twenty)

As see, we got two different answers. In one there is a sign minus, in other the sign minus it is not. Now we will begin to ratiocinate. A similar task is set by the program, the programs are written by programmers. I doubt that they remember about such nuances of school mathematics, as a sign is minus in the results of deduction of numbers. Therefore I suggest to operate by the tested method - by a scientific method. We will enter in a window numbers 20 (twenty) without a sign minus.

If Sim-Sim accepted our answer and opened access to treasures of the Internet, our experiment is completed. If a window answered us, that we are not right, then this iron will give out other pair of numbers to us.

Now we already the experienced users of this window. If it is again written us, for example, "Enter numbers the difference of numbers 0 (zero) and 16 (sixteen)", then we already know exactly, that it is needed in a window to enter - 16 (minus sixteen), with a mark minus ahead.

0 - 16 = -16

(zero minus sixteen evened minus sixteen)

If a window will write something type "Enter numbers the difference of numbers 1 (one) and 0 (zero)", then we without every vibrations enter a number 1 (one). In fact in this case and from the first number to take away second, and from a greater number to take away less, give an identical result is a positive number, without every signs minus.

1 - 0 = 1

(one minus zero evened one)

For all pair of numbers, if the first number anymore than second, a result will always be positive. For example:

20 - 14 = 6

(twenty minus fourteen evened six)

In a window it is needed to enter a number 6 (six, it a number is such).

In case if the program will take in head to flash the erudition and will give out to you a task "Enter numbers the difference of numbers 0 (zero) and 0 (zero)", not frightened and bravely enter a number 0 (zero)!

0 - 0 = 0

(zero minus zero evened zero)


Lighthouses for blondes. All, who searches answers for a question "That means enter the difference of numbers?" - you need to pass to this page!