The product of infinity and zero is undefined. This is because infinity is not a number, and therefore standard arithmetic operations don't apply to it in the same way as they do with ordinary numbers.
Understanding the Concept
The concept of multiplying infinity by zero often leads to confusion. Here's a breakdown:
- Infinity is not a number: Infinity represents a concept of something without any bound or limit. It is not a point on the number line.
- Standard Arithmetic Doesn't Apply: Because infinity isn't a number, multiplying it by a concrete number like 0 doesn't have a standard result.
- Indeterminate Form: In calculus, the expression 0 × ∞ is called an indeterminate form. This means that the limit of a function with the form of 0 multiplied by a function that approaches infinity cannot be determined just by looking at the expression; further analysis is needed.
Why is it Undefined?
Consider the following:
| Operation | Resulting Number | Explanation |
|---|---|---|
| 5 x 0 | 0 | Any number multiplied by zero is zero. |
| 100 x 0 | 0 | Any number multiplied by zero is zero. |
| Very Big Number x 0 | 0 | Any number multiplied by zero is zero. |
| Infinity x 0 | Undefined | Because Infinity is not a number, rules of standard arithmatic don't apply |
According to the reference, calculating the product of two numbers does not exist with infinity multiplied by zero, as infinity is not a number.
Conclusion
The expression "infinity multiplied by zero" is an indeterminate form and does not yield a defined numeric result. It's not equal to 0, 1, infinity or any other defined number.
