In the world of Mathematics, there are many rules and if we break these rules many strange results are possible. One of these rules is that we cannot divide any number by zero. But have you ever wondered why we can't do so? Or what will happen if we do so? So, in this session, we will be finding the answers to these questions. Without any delay let's get started...
Let's first see a basic thing:
10÷5=2
10÷2=5
10÷1=10
10÷0.5=20 and so on
So, from this, we conclude that dividing by smaller and smaller numbers gives bigger and bigger answers. The below graph can explain it more properly:
The smallest number is 0, which means that if we divide any number by 0, we will get the biggest that number i.e., infinity (∞), isn't it? But this is not possible. Now to question arises why?
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Now, to know the answer we need to know what division is.
10÷2 could mean how many times 2 is added to get 10 i.e., 2+2+2+2+2=10. Adding five times 2 results in 10. We can also say that, two times what is 10. If we multiply any given number by x, we can ask if there's a new number we can multiply by afterwards to get back to where we started. The new number is called the multiplicative inverse of the number x. For example,3×2=6 and 6×1/2=3. Therefore, the multiplicative inverse of 2 is 1/2 and the multiplicative inverse of 10 is 1/10. Now see this: 3×1/3=1 and 10×1/10=1. So, the product of the number and its multiplicative inverse is 1. If we want to divide by 0, we need to find its multiplicative inverse which should be one over zero (1/0). This should be a by which multiplying 0 should be one, but multiplying any number with zero will give zero only. So, such a number is not possible and zero doesn't have any multiplicative inverse.
This makes all things tough. Well, mathematicians have broken rules before. For example, for a long time, there was nothing as taking of square roots of negative numbers but mathematicians defined the square root of negative ones as I, opening a whole new world of complex mathematics. So, if they can do that then why not us? Let's take the symbol of infinity (∞) as one over zero (1/0). Just imagine that you don't know anything about infinity and start this experiment.
Based on the definition of multiplicative inverse
0×∞=1
(0×∞) + (0×∞) = 2
(0+0)×∞ = 2 (by the distributive property the left side of the equation can be rearranged)
0×∞ = 2 (as 0+0 is zero only)
We have already defined this (0×∞=2) as equal to 1 in the starting step but this equation is telling that it is equal to 2. So, by this, we conclude that 1=2 is wrong in the world of numbers. But if we do this thing with other numbers such as 3, 5, 10, 99 e.t.c., we will find that all numbers are equal to each other and this will break the whole world of numbers.
Conclusion
So, we conclude that it's not that great to divide with zero and if we do so, it will give incredible results. So, we can't divide by zero and if it is asked that any number divided by 0 is what, then the answer will be 'not defined.
I hope that you have understood why we can't divide by zero and for more such content keep watching my blog. Thank you for Reading and keep learning.