Question

Why is infinity divided by infinity undefined?

Answer 1

Dividing infinity by infinity is undefined in mathematics because infinity is not a specific value and can be infinitely large or small. Division by infinity does not provide a unique answer.

Step-by-step explanation:

Dividing infinity by infinity is undefined because infinity is not a specific number or value. It represents an unbounded quantity that can be infinitely large or infinitely small. In mathematics, division by a specific number can be defined, but division by infinity is not defined because it does not provide a unique answer.

For example, suppose we have two functions: f(x) = x^2 and g(x) = x. As x approaches infinity, both functions become infinitely large. However, if we divide f(x) by g(x) and simplify the expression as x approaches infinity, we get the limit of f(x)/g(x) = x^2/x = x. In this case, the division of infinity by infinity is not undefined, but it equals x, which represents infinity.

Therefore, the division of infinity by infinity is not well-defined in mathematics.

Answer 2

Infinity divided by infinity is undefined because infinity is not a number and cannot be treated as one in mathematical operations. In mathematics, division is a process that involves finding the ratio between two numbers. However, infinity is not a number and has no finite value, so it cannot be used as the denominator or numerator in a division operation.

When dividing infinity by infinity, you are asking for the ratio of two quantities that are both infinite, and the result is not well-defined. The concept of infinity can be useful in certain mathematical contexts, such as limits and calculus, but it cannot be used as a number in the usual sense.

In mathematical terms, the expression infinity divided by infinity is considered indeterminate and has no defined value. This is why it is undefined in mathematical analysis.

Step-by-step explanation: