Why can’t you divide by zero? – TED-Ed

Translator: Hanan Zakaria Auditor: Eman Sabry within the mathematician Many unusual outcome are possible once we alternate the laws. But there is one rule that all of us were warned to not violate: do not divide with the aid of zero. How a simple combo of numbers we use daily A easy mathematical recreation to reason all these issues? Usually, divide through smaller and smaller numbers It offers you bigger and higher outcome Ten divided with the aid of two equals 5 Ten divided by means of one equals ten Ten divided via one million equals 10 million and so on. So it looks as if you divided the numbers That keeps shrinking to zero, The outcomes will grow to the largest feasible. So is not the influence of ten divided by zero the infinity? This may increasingly seem reasonable. But all we know is that if we divide 10 The quantity is nearly zero The influence tends to be infinity. And that is now not like we stated dividing the quantity 10 with the aid of zero Equal infinity. Why now not? Well, let’s take a better appear on the definition of division. With the aid of pronouncing 10 divided through 2, we imply: "How typically do we need to add 2 to get 10?" In other words, "What quantity if we multiply it by way of 2 will we get 10?" Dividing with the aid of the number is the opposite procedure of multiplying by means of that quantity, within the following method: If we multiply any quantity through the number of x we are able to ask if there’s a new quantity that we will multiply later Let’s get the quantity that we began with. If there is, the brand new quantity will be the reciprocal of the quantity "x" For illustration if you happen to multiply 3 by using 2 to get 6, Then which you could multiply 6 with the aid of 1/2 to get three again. So the reciprocal of 2 is half of of one, The reciprocal of 10 is one in ten. And as you noticed, the manufactured from any quantity expanded with the aid of its inverse it is continuously one. If we wish to divide via zero, We have to to find its the other way up, Which will have to be one with the aid of zero. Must be a quantity when improved through zero The outcome is one. But because any number we multiply through zero continuously offers us a zero, The possibility of a number like this is impossible, as a result, zero just isn’t inverted. And but is that every one right? In any case, mathematicians broke the principles earlier than. For instance, over a long time, There used to be no such thing as a rectangular root of negative numbers. However then scientists outlined the square root of bad quantity As a new number known as "i", This opened the door to a new world of arithmetic for intricate numbers. So in the event that they would do that, Why are not able to we also create a brand new rule? Shall we say that infinity image means one over zero, and notice what occurs? Let’s are attempting to do this, assume that we do not know something about infinity. Situated on the definition of the reciprocal of the number, Then zero instances infinity will have to provide us one. Which means zero occasions infinity plus zero in infinity have to be equal to two. Now with the distribution function, The left a part of the equation will also be rearranged in an effort to grow to be zero plus zero times the infinity. And considering zero plus zero is definitely zero, This will also be shortened to zero at infinity. Regrettably, we’ve got set this as equal to 1, whilst the opposite part of the equation remains to be equal to 2. So, one equals two. Somewhat strange, but now not necessarily improper, it’s only no longer authentic in our normal world of numbers. There is still a way this can be mathematically right. If one, two, three and all other numbers are equal to zero. But that infinity is zero it is vain to mathematicians and any individual else. Actually there may be anything called a Ryman ball Which involves dividing by using zero in an additional approach, but this is a story we are going to inform in an extra episode. In the interim, divide through zero evidently not very mighty. But this must now not discourage us and try to break mathematical rules to look if we can invent new worlds to explore.

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