Zero divided by infinity is 0.
When we consider 0 divided by infinity (0/∞), we're essentially asking what happens when we divide zero into an infinitely large number of pieces. Regardless of how many pieces we divide zero into, each piece will still have a value of zero.
Here's why:
Imagine you have nothing (zero). No matter how many times you try to split that "nothing," you still end up with nothing. Whether you divide it by 2, 100, or even an infinitely large number, the result remains zero.
Formal Definition (Limit approach):
In calculus, this concept is often encountered in the context of limits. If we have a function where the numerator approaches 0 and the denominator approaches infinity, the limit of that function is generally 0. We can express this as:
lim (x -> ∞) 0/x = 0
Examples:
- Imagine dividing 0 apples among an increasing number of people. As the number of people approaches infinity, each person still receives 0 apples.
- In a mathematical context, consider the function f(x) = 0/x. As x gets larger and larger (approaches infinity), f(x) gets closer and closer to 0.
Therefore, 0/∞ = 0
