If n equals 8 why is n divided by 0 undefined?

Answer 1

Undefined: You cannot divide by zero

Answer 2

Because any number can be divided by "0" an infinite amount of times; this means you could spend the rest of your time on earth counting the number of times, so mathematicians (everyone will tell you they are lazy) decided to make it a rule to not divide by the number 0, which really isn't a number at all.

A number is a count of something, if you have 0 of something then you have nothing to count, therefore you are dividing n or 8 by nothing at all. What happens if you drop your variable "n" into a black hole? Essentially the answer is infinity and this is a useless value to give to anything on earth if you hope to come to some sort of conclusion to whatever problem you come across which you are using math to solve.

In a more mathematically rigorous context, it can be said that 0 is not considered what we call a natural number, or a quantity that can naturally occur. Natural numbers are all positive integers like 1, 2, 3, and so on. The number 0, or rather the concept of 0 was discovered some time ago in India, and that is the oldest recorded time that I know of when the idea of 0 came up.

Using calculus, you can show that any number a divided be zero, such that a is not equal to 0 will tend towards positive or negative infinity. Imagine some function f(x) = a/x, where a is not equal to 0. If you attempt to evaluate the limit as x approaches 0, it will be undefined and no algebraic manipulation can work around that. Using analytic geometry, you can actually observe the graph of a/x and tell very easily with little knowledge of math that the function approaches infinity from one side and negative infinity from the other side (which side for which respective infinity depends on whether a is positive or negative). because a/x is not continuous at x=0, and there exists no single limit as x approaches 0, we say that and number a divided by 0 will be undefined. Oddly enough, a/x^2, where a is not equal to 0, does have a limit as x approaches 0. if a is positive, it is positive infinity and if a is negative it is negative infinity. So while some number a divided by 0 squared may not necessarily be defined, the limit is.

We've studied the number 0 for quite some time now, but it's probably best in any case to consider it undefined, because it can't truly be considered a number. 0 however is not completely useless in mathematics just because it's not an actual number. Just like infinity and imaginary and complex numbers, we've found many uses for 0, even at the elementary question, "What is a minus a?".