Mathematics. Why we can not divide any number by 0?

After I started writing about math, I saw the paragraph that I shared below. It was discouraging but also it was utterly true.

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

Okay, why we can not divide any number by 0?

Technically, dividing by zero is a division operation where the divisor or denominator is zero. We can express this division formally as as a/0 {a over zero} where a is the dividend (numerator). For mathematics, the expression a/0 has no meaning.

Definition of Numerator: The number above the line in a common fraction showing how many of the parts indicated by the denominator are taken, for example, 2 in 2/3.

Such an important property: Zero times anything must be zero.

Image for post
Image for post

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

Normally when we see an equation like this …

Image for post
Image for post

we just evaluate what’s in the parentheses first, then solve it:

Image for post
Image for post

With the distributive property, we multiply the ‘5’ first”;

We distribute the 5 to the 7 then to the 4.

Image for post
Image for post

Then we need to remember to multiply first, before doing the addition!

Image for post
Image for post

Now we can proof that why anything times 0 equal to 0.

Apply this property to zero and something strange happens.

We know that 0 + 0 = 0.

Image for post
Image for post

It doesn’t matter how many groups of zero you have, because they would never add up to ten since 0+0+0+0+0+0+0+0+0+0 = 0.

Image for post
Image for post

You could even have one million groups of zero blocks, and they would still add up to zero. So a number multiplied by zero is the same thing as multiplying by (0 + 0).

Let’s take 7 as an example and multiply 7 and 0.

7 x 0 has to be equal to 7 x (0+0). By the distributive property

Image for post
Image for post

7 x (0 + 0) will be the same thing as 7 x 0 + 7 x 0. Thus

7 x 0 = 7 x 0 + 7 x 0.

Image for post
Image for post

So whatever 7 x 0 is, when you add it to itself, it stays the same. It looks like 0!!!

Anyway let’s solve the equation. We should subtract 7 x 0 from each side of the equation and we see that 0 = 7 x 0.

Image for post
Image for post

Thus, no matter what you do, even if you use one billion or 32 to multiply by 0, you will get 0!

Now, it is time to prove that dividing by 0 is undefined.

We saw in the previous example that 7 x 0 = 0. Thus to undo the multiplication, we can claim that (7 X 0)/0 will get us back to 7. WHY?

Image for post
Image for post
10/2 = 5   This means that 5 x 2 = 1027/9 = 3   This means that 3 x 9 = 277/1 = 7    This means that 7 x 1 = 75/0 = ?    This would mean that the answer x 0 = 5, but 
anything times 0 is always zero. CONTRADICTION!

Likewise, (9 X 0)/0 should get us back to 9, and (24 X 0)/0 should equal 24. But 9x0 and 24x0 and 5x0 each equal zero, as we saw — so (9 X 0)/0 equals 0/0, as do (24 X 0)/0 and (5 X 0)/0. So this means that 0/0 equals 9, but it also equals 24, and it also equals 5. This just doesn’t make any sense.

Image for post
Image for post

As you can see, if you try to divide by zero, you can destroy the entire foundation of logic and mathematics.

Now prove that 1=2 or 2+2=5.

Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better. alikayaspor@gmail.com