What is 0 divided by 0?
Understand the Problem
The question is asking about the result of dividing zero by zero. This is a fundamental question in arithmetic concerning the definition and limitations of division when zero is involved.
Answer
$0/0$ is indeterminate.
Answer for screen readers
$0/0$ is indeterminate.
Steps to Solve
- Define Division
Division is the inverse operation of multiplication. That is, $a / b = c$ means that $a = b \cdot c$.
- Apply the definition to $0/0$
Let $0/0 = x$. Then, according to the definition of division, $0 = 0 \cdot x$.
- Analyze the equation $0 = 0 \cdot x$
Notice that $0 \cdot x = 0$ is true for any value of $x$. For example, $0 \cdot 1 = 0$, $0 \cdot 2 = 0$, $0 \cdot (-5) = 0$, etc.
- Conclusion
Since any value of $x$ satisfies the equation $0 = 0 \cdot x$, the expression $0/0$ does not have a unique value. Therefore, $0/0$ is considered indeterminate.
$0/0$ is indeterminate.
More Information
The expression $0/0$ is not simply "undefined"; it's more specifically classified as "indeterminate." This distinction is important in fields like calculus, where limits approaching $0/0$ require further analysis to determine if a meaningful value can be assigned.
Tips
A common mistake is to assume that $0/0 = 1$, based on the idea that any number divided by itself is 1. However, this rule doesn't apply when the number is zero because division by zero is undefined. Another mistake is to think $0/0 = 0$ because zero divided by any number yields zero but the denominator is zero, making it an invalid operation.
AI-generated content may contain errors. Please verify critical information
