Why dividing by zero is undefined?
Try this on your calculator
5/.01 = ..
5/.00001 =
5/.0000001 =
notice I am making my divisor smaller and smaller, almost zero and what is happening to your answer?
The closer my divisor gets to zero, the larger the answer.
So when I could actually divide by zero, then the answer should be infinitely large
which of course is not a number, thus we call it "undefined"
Or, consider this. Suppose 4/0 = x for some value of x.
To clear the fraction, we get 4 = 0*x
But 0 times any number is zero. So, there is no possible value of x for which 0*x = 4. (Or any other nonzero value)
Dividing by zero is considered undefined in mathematics because it leads to inconsistencies and contradictions within the number system. To understand why dividing by zero is undefined, let's break it down step by step:
1. Division is essentially the inverse operation of multiplication. When we divide a number by another number, we are asking "How many times does the second number fit into the first number?"
2. When we divide any number by a nonzero number, such as 8 divided by 4, it means we are asking "How many times does 4 fit into 8?" The answer is 2, because 4 can go into 8 two times.
3. However, when we try to divide by zero, such as 8 divided by 0, the question becomes "How many times does 0 fit into 8?" This question does not have a meaningful answer.
4. The reason it doesn't have a meaningful answer is because there is no number that we can multiply by 0 to obtain a nonzero number. In other words, there is no solution to the equation 0 * x = 8.
5. If we were to assign a value to 8 divided by 0, it would lead to inconsistencies and contradictions. For example, if we say that 8 divided by 0 equals 4, then we would also have to say that 0 multiplied by 4 equals 8. But we know that any number multiplied by 0 is always 0, not 8. This contradiction shows that dividing by zero cannot be defined consistently.
In mathematics, we rely on consistency and logical coherence to ensure that our number system is reliable and can be used in various calculations and applications. By considering division by zero as undefined, we maintain the integrity and consistency of the number system.