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

Translator: Hanan Zakaria Auditor: Eman Sabry In the mathematician Many strange results are possible when we change the laws. But there is one rule that we all have been warned not to violate: Don't divide by zero. How a simple combination of numbers we use every day A simple mathematical exercise to cause all these problems? Usually, divide by smaller and smaller numbers It gives you bigger and bigger results Ten divided by two equals five Ten divided by one equals ten Ten divided by one million equals 10 million and so on.

So it looks as if you divided the numbers That keeps shrinking to zero, The result will grow to the largest possible. So isn't the result of ten divided by zero the infinity? This may seem reasonable. But all we know is that if we divide 10 The number is close to zero The result tends to be infinity. And that's not like we said dividing the number 10 by zero Equal infinity. why not? Well, let's take a closer look at the definition of division. By saying 10 divided by 2, we mean: "How many times do we have to add 2 to get 10?" In other words, "What number if we multiply it by 2 will we get 10?" Dividing by the number is the inverse process of multiplying by that number, In the following way: If we multiply any number by the number of x We can ask if there is a new number that we can multiply later Let's get the number that we started with. If there is, the new number will be the reciprocal of the number "x" For example if you multiply 3 by 2 to get 6, Then you can multiply 6 by half to get 3 again.

So the reciprocal of 2 is half of one, The reciprocal of 10 is one in ten. And as you noticed, the product of any number multiplied by its inverse It is always one. If we want to divide by zero, We must find its upside down, Which should be one by zero. Must be a number when multiplied by zero The result is one. But because any number we multiply by zero always gives us a zero, The possibility of a number like this is impossible, Therefore, zero is not inverted. And yet is that all right? After all, mathematicians broke the rules before. For example, over decades, There was no such thing as a square root of negative numbers. But then scientists defined the square root of negative number As a new number called "i", This opened the door to a new world of mathematics for complex numbers. So if they could do that, Why can't we also create a new rule? Let's say that infinity symbol means one over zero, And see what happens? Let's try to do that, Imagine that we don't know anything about infinity. Based on the definition of the reciprocal of the number, Then zero times infinity should give us one. This means that zero times infinity plus zero in infinity must be equal to two. Now with the distribution feature, The left part of the equation can be rearranged In order to become zero plus zero times the infinity. And since zero plus zero is definitely zero, This can be shortened to zero at infinity. Unfortunately, we have set this as equal to one, While the other part of the equation is still equal to 2. So, one equals two. A little strange, but not necessarily wrong, It is just not true in our ordinary world of numbers. There's still a way this can be mathematically correct. If one, two, three and all other numbers are equal to zero. But that infinity is zero It is useless to mathematicians and anyone else. In fact there is something called a Ryman ball Which includes dividing by zero in a different way, But this is a story we'll tell in another episode.

For the time being, divide by zero clearly Not very effective. But this should not discourage us And try to break mathematical rules To see if we can invent new worlds to explore.

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