Division by zero is an undefined operation in mathematics, meaning that it is not possible to find an answer when attempting to divide any number by zero. This is because division involves the process of determining how many times one number can be contained within another, and this cannot be done when the divisor is zero. For example, if we wish to divide 6 by 2, we can perform repeated subtraction to find the answer:
6 – 2 = 4 4 – 2 = 2 2 – 2 = 0
We have subtracted 2 from 6 three times, which means that 6 divided by 2 is 3. However, if we attempt to divide 6 by 0, we cannot use repeated subtraction to find the answer because there is no number we can subtract from 6 an infinite number of times to arrive at 0. This is why division by zero is undefined.
You may have heard some people say that 1/0 equals infinity, but this is not strictly true. Rather, it is more accurate to say that the limit of 1/x as x approaches 0 is infinity. This means that as x gets closer and closer to zero, the value of 1/x grows without bound and becomes infinitely large. This can be written as:
lim (x → 0) 1/x = ∞
However, it is important to understand that this does not mean that 1/0 is equal to infinity. It simply means that the function 1/x grows infinitely large as x approaches zero.
In summary, division by zero is undefined in mathematics and it is not possible to prove that 1/0 equals infinity. While the limit of 1/x as x approaches 0 is indeed infinity, this does not mean that 1/0 is equal to infinity.