2.08.2011

Division by zero - the question formulation

Division by zero is maybe - to such conclusion we have come. But to solve a problem about division of number into a zero we and could not. Then let's solve not a specific target on division of number into a zero, and a zero problem as a whole. We begin all from the very beginning.

What is the zero? All-knowing Wikipedia says that the zero is a number. This number designates a point on a numerical straight line which separates positive numbers from the negative. Give also we will look at this well-known numerical straight line in which the dog on a nickname "Zero" is buried.

Number line. Mathematics for blondes.
Number line
And now we will look, as the zero in the basic mathematical operations behaves agrees the standard mathematical rules:

a + 0 = a

0 + a = a

a - 0 = a

0 - a = -a

a - a = 0

a · 0 = 0

a : 0 = ?

0 : a = 0

0 : 0 = ?

In that mathematicians are mistaken, including division into a zero impossible, we have already understood. Instead of whether and mathematicians are mistaken in other places at the formulation of results of mathematical actions with zero? Quite probably that some from resulted above equalities are false statements.

The problem with zero in the mathematician dares simply and gracefully, in style of blondes. Therefore mathematicians to such never will guess. Here the sober and critical sight of the person from outside, without fanatical belief in the received mathematical knowledge is necessary. Blondes for a zero solution of a problem approach as well as possible. About the mathematician they have the most general representations. Their mentality differs from the standard.

Whether you can find a solution of a problem with zero? The variants of the decision leave in comments.

2.07.2011

Division of number into a zero

Last time we have considered possibility of division into a zero, and have come to conclusion that Division by zero is maybe. But it was only the half of a problem of division into a zero which decision we undertook. There is one more set of the equations of division into a zero which we are simply obliged to consider.

We have very cheerfully laughed over Wikipedia, now has come turn of all of the others to laugh over us. We will try to answer on a question that will turn out if to try to divide any number into a zero. That the number as a result cannot turn out, we have neatly noticed. Then, what can turn out? Not clearly that. We will designate it "not clearly that" which turns out as a result of division of number into a zero, a question mark. At us such small set of the mathematical equations will turn out:

a : 0 = ?


0 · ? = a


a : ? = 0

Now the equations received from the equation of division of number on a zero, we will try to sound and compare to the rules accepted in the mathematician. If a zero to divide on not clear that, any number as a result will turn out. As we know from the previous message, it is possible to assume only that any number turns out as a result of division of zero into a zero.

If any number to divide on not clear that, the zero as a result will turn out. As we know, in the mathematician all occurs just what isn't needed: the zero turns out as a result of division of zero into any number.

We include logic of blondes and we start to think, how to us with this most "to be not clear that"? How, how? Yes in any way! We will substitute instead of a question mark a zero - and there are not problems. Then at us rather nice equations with zeroes will turn out:

a : 0 = 0


0 · 0 = a


a : 0 = 0

Here! The first and last equations coincide now and it is not necessary nothing to think out! Well, and that the zero increased by a zero at us equals to any number, means nothing. There should be whence that any numbers? It is such sleeve of the mathematician-conjurer from which it always gets them. "Let any number is given us..." All around sit, mouths поразевали, have listened openmouthed, eyes around ransack in search of any number, and mathematics in the meantime, imperceptibly, from the sleeve, gets this most any number and shows to spectators. All spectators in delight clap in palms. But we that know that in a sleeve at the mathematician division of zero into a zero is hidden. Or multiplication of a zero to a zero? Oh, with this zero absolutely it is possible to get confused.

Here we, as real mathematicians, have come to the equation:

0 : 0 = 0 · 0 = a

And after all all know that any number increased by a zero, equals to zero, instead of any number. Again at all of us will laugh. Mathematicians this problem cannot already solve some hundreds years, that already only did not think out. Now we stand near to them in a deaf corner in which ourselves have tired out ourselves and from which there is no exit, we look against each other and we wipe the snotty noses.

It is possible to put, of course, instead of a question mark an infinity badge. But what such infinity? Basically, this same any number, only very much the big. Means, this variant is not necessary.

As we see, the problem with division into a zero does not dare. Though we have come to a conclusion that the decision should be.

Let's next time try begin all with the beginning. Only not from that beginning from which, and division into a zero begins with that beginning with which the zero begins.

2.05.2011

Division by zero is maybe!

Division by zero is considered impossible. Why? Because so mathematicians consider and learn others to think in the same way. Why mathematicians so consider? And here it is already interesting question. Everything that you will read further, can show to the friends and girlfriends, but do not take in head to show to mathematicians. Mathematicians can consider that you it is cleverer than them and terribly and cruelly to you will revenge. And you after all perfectly know that such revenge. Here when become the mathematician then can argue on a theme of division into a zero. Now we will try to understand, why division by zero is impossible?

We open a page of Wikipedia "Zero" (in Russian language) and attentively we read that to us offers collective reason. Mathematicians take number a and divide it into 0 (zero). Include the mathematical logic Further and begin reasonings. Let as a result of division the number c has turned out. In this case at number multiplication c by zero we should receive number a. But at multiplication to a zero of any number the zero as a result turns out. From this it follows that the number c cannot be result of division of number an by zero.

Personally I think hardly. We will try to write down all it easier:

a : 0 = c


c · 0 = a

Yes, really, not beautifully it turns out, especially wrong second equality. So in the mathematician does not happen. After all all know that any number increased by a zero, equals to zero.

Here it is a high time to remember a small lesson of history. Once, very long time ago, ALL considered that the Earth is a flat island in the middle of an ocean chasm which keeps on backs of three whales. This island is the World Center round which, on heavenly spheres, different features rotate: the sun, the Moon, asterisks.

Division by zero maybe! Earth on three whale. Mathematics  for blondes.
Division by zero is maybe!
Those who thought differently, it was accepted to burn on fires. Now we became more civilised, on fires we burn nobody. But to put in you the two or fill up you at examination can very simply.

And the lesson of this history says: ALL can be mistaken. If ALL around will start to be hung up, I hope, you not begin to do the same? In other words, the opinion of one person or opinion of the majority of people CAN be ERRONEOUS. If we do not acquire this lesson of history, history to us it will give once again, and once again until we will not grow wiser. Apparently, the situation with division into a zero is a repetition of lesson already passed by us.

a · 0 = 0

Now we will execute transformations and we will receive:

0 : a = 0

0 : 0 = a

The first turned out line corresponds to a mathematical rule which says that if a zero to divide into any number, the zero as a result will turn out. Concerning the second line of mathematics speak, expression a zero to divide into a zero it is not meaningful, as cannot be defined. Hi-hi, and we have defined that the zero деленный on a zero equals to any number. To which number? And what number is necessary to you, such and write. By the way, one rich dad searched to itself in the firm of chief accountant. To all applicants, besides other, it asked a question: "How many will be twice two?". For work it has accepted the person who has answered this question with the question: "And how many it is necessary to you?".

And so, mathematicians want to see concrete number, instead of the general phrase as a result of division by zero. For this reason they consider division by zero impossible. Here it is a high time to remember the second lesson of history.

You about integrals heard? If is not present, it is not terrible. It looks so: the uncertain integral something equals to something plus a constant. What is "constant"? This any number which we do not know. Yes-yes, just the same unknown number, as well as result of division by zero. So, the integral is not meaningful? Has not only sense, but also it is often applied in engineering calculations. Focus consists that the uncertain integral is only the theory. In practical calculations certain integrals are applied. When business reaches the certain integrals, all problems with a constant, that is unknown number, disappear. As a result of integration quite concrete numbers turn out.

Why it is possible to find integral and to divide into a zero it is impossible? I think that in due time engineers have come to mathematicians on a throat and the decision of a concrete problem have demanded. Mathematicians have thought up integrals and ways of their finding. It has saved to mathematicians life.

Why engineers so will not make with division by zero? To the decision of practical problems with division by zero to our engineers still as to babies to pension. Engineers simply have not grown to this level of knowledge and technics. And to mathematicians division by zero and so will descend. What difference that you to learn? Nobel Prizes do not give to them so what for once again in vain to strain.

Considering the second lesson of history, it is possible to declare with all responsibility that arguments of mathematicians concerning impossibility of division by zero are not accepted, as in a similar case with uncertain integrals were them, mathematicians, are denied.

Division by zero is maybe. We are not able to divide into a zero yet. Anything shameful in it is not present. The third lesson of history. Once people in general were not able to divide. Even number on number. Anything, have learnt both to divide, and to integrate. We will learn and on a zero to divide. Certainly, if for it us will not burn on fires. Or to arrange round us wild dances of shamans under a tambourine, inspiring us the sacred spells "Division by zero it is impossible!", "Division by zero is not meaningful!".

Enter number, how many there will be a factorial of three

"Enter number, how many there will be a factorial of three" Ogo! Here it is an ambush for blondes! Judging by that is written "enter number" is a site of any pervert from mathematics asks to enter into a window number. I would be frightened of such request! Same it is necessary to be such sadist that the visitors by means of a torture factorial to arrange! And it would be desirable to ask: "And you, the clever man, can count a factorial of four?! Or without the calculator poorly?!" Is not present, with this disgrace it is necessary to struggle. Anybody from Internet users is not obliged to know factorials - the Internet exists for all. It is obvious discrimination of blondes!

With a view of struggle against similar mathematical rudeness, we will create the small table of factorials for the aid to poor blondes and not only to it.

0! = 1
1! = 1
2! = 1 х 2 = 2
3! = 1 х 2 х 3 = 6
4! = 1 х 2 х 3 х 4 = 24
5! = 1 х 2 х 3 х 4 х 5 = 120


And so, the zero factorial is equal to unit, unit factorial is equal to unit, the factorial of two is equal to two, the factorial of three is equal six, the factorial of four is equal twenty four, the factorial of five is equal hundred twenty. I think, it will be quite enough for personal self-defence on the Internet.

By the way, as chance offers can ask those, who considers itself strongly literate, whether they know, how many figures at a factorial, well... For example, two hundred fifty five? In this number of five hundred five figures!!!

255! = 3350850684932979117652665123754814942022584063591740702576779884286208799035732771005626138126763314259280802118502282445926550135522251856727692533193070412811083330325659322041700029792166250734253390513754466045711240338462701034020262992581378423147276636643647155396305352541105541439434840109915068285430675068591638581980604162940383356586739198268782104924614076605793562865241982176207428620969776803149467431386807972438247689158656000000000000000000000000000000000000000000000000000000000000000

This number is five times longer, than the well-known number googol, in which only one unit and hundred zeroes. And at us five hundred five it is not simple zeroes, and different numbers)))

I hope, to anybody from you will not offer: "Enter number, how many there will be a factorial of two hundred fifty five")))

2.03.2011

Bermuda triangle and eternal youth

The Bermuda triangle is, we already spoke about it, when considered a triangle. With the Bermuda triangle it is connected a lot of mysterious and terrible stories. That in these stories truth, and that a usual advertising gimmick for advertising of favourite, - is difficult to understand. The Bermudas triangle on a card looks so:

Bermuda triangle and eternal youth. Mathematics for blondes.
Bermuda triangle
We will not remember all stories connected with the Bermuda triangle, and to assort them on stones. On the Internet it is information full. We will consider only one, curious enough, a case connected with the Bermuda triangle.

The passenger plane "the Boeing 727" with passengers onboard from Atlantic ocean flies up to the airport of Miami. According to rules, the crew spends verification of hours with land services. In 20 minutes the plane disappears from screens of a radar. Radio contact to plane has interrupted. In 10 minutes after disappearance, the plane again appears on screens of a radar. The plane has safely landed. A whole hours passengers and the plane lagged behind for 10 minutes. Anybody from crew or passengers unusual has not noticed anything.

Truth it or fiction? Our habit always and all to say lies, and also the mania of government officials to code all, does not give us possibility precisely to answer this question. If it is fiction - it is a pity. If it is truth - before us interesting enough possibilities open.

Present that you have come to school. Today at you control on the mathematician. The lesson begins, the teacher gives out all the task. After that you imperceptibly get a small charm from the beautician, press a button - the teacher disappears. You easy solve all examples and problems. By the end of a lesson the teacher appears again. With astonishment looks at the watch in a class - shout, ор, but the lesson already comes to an end and it is necessary to collect examinations. Naturally, control all have written this perfectly well!

Whether it is possible to use such charm what to keep the youth? Yes. It is necessary simply most to disappear for some time. All around live, grow old - and you here are not present. It is possible to disappear for the period of vacation. And it is possible to disappear and for all academic year - how many the time you can save! Present, your girlfriends ugly old cows, and you - young and beautiful! Here the main thing - not to overdo. Passing employment, you risk to turn in обезьянку from a zoo. With you all will be photographed, feed you with bananas, and you nothing will not think from this that round you occurs.

And if it is serious, the similar charm will help to keep lives to people in extreme situations. For example, if urgent medical aid is necessary to the person, and this help it is necessary to wait. That the person has not died, you do so that it has disappeared and return it already after occurrence of doctors which can rescue this person.

Fantasy it or real possibility? From the point of view of mathematics here all speaks simply enough. If you have a desire in it to understand - write in comments. We can plunge into this mathematical jungle. But consider that mathematics specific enough science. Look how simply to become the millionaire from the point of view of mathematics: scrape out from a purse all money which at you are, and add to them one million dollars. All - you the proprietress of treasured one million. Where and as you this one million dollars take - mathematics at all does not excite. But the mathematics can prompt variants. It is possible to find one rich man which will give you one million. And it is possible to find one million not rich man which will give to you on one dollar, the same one million dollars as a result will turn out.

You ask, and how eternal youth? Elementary. Disappear from this world young and beautiful. Also do not come back any more never. Than this way differs from death? From our point of view - practically than. So for preservation of eternal youth it is necessary to look for other recipes.

2.02.2011

Types of triangles

Types of triangles differ on clothes. Here when you look at the person, you, first of all, estimate it clothes and at once much becomes clear to you - what dirty trick from this person can be expected. Precisely as well at triangles. However, triangles have only two clothes which can be estimated simultaneously are corners and the parties. On a picture of a triangle it looks here so:

Types of triangles. Rectangular  triangle, right triangle, obtuse and acute triangle. Mathematics for Blondes.
Types of triangles.
The very first triangle on a picture - a right triangle. It is called so because this triangle has one right angle. Two right angles at a triangle does not happen - remember the triangle theorem? Correctly, if two corners take away to themselves on 90 degrees, to the third corner nothing does not remain. And what can be a triangle with two corners? There are no two-coal triangles. Everything, the theorem of a right angle in a right triangle for blondes is proved!

Types of triangles. Scalene, equilateral and isosceles triangle. Mathematics for Blondes.
Types of triangles.
It is possible to name a right triangle a triangle of Pythagor, on it Pythagor proved the well-known Pythagorean theorem. Let for Pythagor a right triangle also remains. Further on a picture at us the acute triangle is drawn. In it all three corners sharp, as female uvulas. Means, this triangle female. The top part of portrait gallery of triangles comes to an end with an obtuse triangle. This triangle has one big corner, and this corner stupid. It is a man's triangle. No, not because men stupid! No! Think. If there is a female triangle, means should be and man's. And all other triangles are already disassembled! There was only this... Here!

In the bottom part of a cloth of a brush of the unknown artist of the XXI-st century we see triangles which differ with lengths of the parties. To the first in the bottom number there is an equilateral triangle - a democracy symbol. Because all three parties at an equilateral triangle of equal length so - they are equal among themselves.

Further the isosceles triangle is drawn. A symbol of grace and beauty of women. At this triangle two parties have identical length. You imagine the woman with hips of different length? Here, and I do not represent. Why an isosceles triangle named so? In honour of blondes of whom mathematicians dreamt, drawing a pencil a triangle that under a hand has got. After all the majority of mathematicians there were no Leonardo's da Vinci's. Instead of fine Mona Liza's at them them isosceles triangles turned out.

The latest triangle - a scalene triangle - a symbol of geometrical tortures. And you thought, it is connected with erudition of this triangle? As though not so! At this triangle the teacher wants to know all three parties of different length and length of each of the parties of a triangle! After tortures by such triangle even Pythagor has not sustained and has told the theorem. In general, the scalene triangle is the most terrible nightmare of pupils on an extent already more than two thousand years.

Triangle names and pictures - it here. Types of triangles and their name.

Mathematics of an inequality

In the mathematician equalities and inequalities are very extended. Whether the inequality can be useful practically to us in an everyday life? Perhaps if you learn to make inequalities of the most simple situations and to analyze them.

Here the most usual situation. You have got acquainted with the guy who was presented to Vasej. Вася has told that it the friend Bill Gates. Here we also will use mathematical principles of construction and the inequality analysis.

First of all, we will remember one mathematical rule - an addition rule. This rule says that from shift composed the sum does not change. Other mathematical rule asserts that at shift of factors product does not change. Here we apply this principle of shift to words of Vasi and we look that at us it has turned out:

(Vasja has told that it the friend Bill Gates) is equal (Bill Gates has told that Vasja its friend)

Now we will analyse both received phrases. You personally are not familiar neither with Vasej, nor with Bill Gates. But Bill Gates - the celebrated personality, therefore you will trust its words much more, than to words of known Vasi any to nobody. The probability of that Vasja REALLY is the friend Bill Gates, is smallest. Hence, we have received an inequality which looks so:

(Vasja has told that it the friend Bill Gates) is not equal (Bill Gates has told that Vasja its friend)

From the phrase analysis it is possible to draw a conclusion that from you something is necessary for this Vasja. If simply to make upon you impression is one. If speech comes about money is another.

Similar reception - to be called as someone concerning the celebrated personality - any swindlers very often use. Especially, when speech comes about money: "the pupil such", "the right hand of that" and so on, and so forth.

If you learn easily and quickly to define situation high lights, mentally to change a situation on opposite and to analyze the received results, it will be much easier to you to make correct decisions.