What is dividing by zero? What is it? It means dividing a number by 0. So, it’s normal division math. Just do it by following the rules. But wait. It’s not so simple as you are thinking. Let me explain a little more.
Let’s consider some examples. Start with multiplying. When we say 3x5 =15, We mean that 3x5 = 3+3+3+3+3. Which means five times three. Similarly when we say 5x3 = 15, we mean that 5x3 = 5+5+5. Which means three times five. So what we can understand from it? We can understand that whenever we want to multiply x and y we have to add y times x.
Let’s move into dividing. When we say 15/3 = 5, we mean that 15/3 = 15–3–3–3–3–3. This means how many times I can subtract 3 from 15 until I get 0. And the result is as you see 5. So that means we can subtract 3 for 5 times from 15 until I get any zero. A similar method goes for 15/5 = 3, which means we can subtract 5 for 3 times from 15 until I get any zero. Like that, when we say 1/0 = ∞, we mean that 1/0 = 1–0–0–0–0–0–0–0–0–0–0–0–0–0–0–0–0–0–0–0–0……….∞, and so on we will find the numerator but not we will find the result. So, that’s why dividing by zero is equal to infinity.
If you find this method quite hard, you can assume another method for understanding. What does 6/2 mean? It means how many 2 is needed to make the number 6. And then if we want to solve it that will be — 6/2 = 2+2+2 -> which makes the total numbers of 2 as a result. So the result is as your see 3. For that, if you consider 1/0 that means how many 0 is needed to make the number 1. So if we want to calculate this by the method given above we will see that — 1/0 = 0+0+0+0+0+0+0+0+0+0+0+0+0+0….+∞, and still, we are finding the number 0 but not result in 1, and we can’t find the actual numbers of 0 to make 1. So the result will be infinity(∞). So that’s why dividing by zero results in infinity.
Now, look at some interesting facts. We say that, 1/0 = ∞. So let’s check some steps. We will go from 1 to 0 continuously according to the number line.
1/1 = 1
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/0.0001 = 10000
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1/0 = ∞;
So we find the result infinity. That’s ok. But now consider another case.
1/-1 = -1
1/-0.1 = -10
1/-0.01 = -100
1/-0.001 = -1000
1/-0.0001 = -10000
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1/0 = -∞;
Wait for what? In this case, we are not going to infinity but we are going to the negative infinity. but this doesn’t make any sense. By dividing by zero we are finding not the infinity, but we are finding totally a random number. Now you can ask that, in the previous para’s I’ve proven that 1/0 is equal to infinity. But now I am saying that it’s not the infinity, it’s a random number. So, what’s the matter?
The actual result is divided by zero is undefined. Not infinity. What is undefined? The undefined means the result is not or can’t be defined and it is undefined able. As we said that we are finding random numbers between ∞ and -∞. And that random number can’t be defined cause that doesn’t exist. So by following the rule we can say that1/0 is equal to infinity but the actual result is undefined. Hope you understand.
Now jump into another interesting part.
1/0 = ∞ , if we apply the side changing rule, we will find that 0x∞ = 1. Ok, that’s alright.
By the above calculation, we can say that-
(0x∞)+(0x∞) =2, right? ok.
Now if we apply the simple arithmetic rules here, we will find that-
0 x (∞) + 0 x (∞) = 2
or, (0+0)x(∞) = 2 (By the distributive law)
or, 0x∞ =2
So, 0x∞ = 2;
But unfortunately, we have already defined that 0x∞ = 1;
So, 0x∞ = 1;
and 0x∞ = 2;
so, it will be 1=2. Yeah. That’s the logic. By the above logic, we can define that 1=2. But is it true really? No away. It is common sense that 1 and 2 are not equal. And it should not be equaled. It is wrong. So, this infinity doesn’t make any sense. It should be undefined which is correct.
So, that’s why dividing by zero is undefined. Hope you understand that.
N. B: If you have any queries please inform me. And also if you find any mistake, forgive me and inform me quickly.
