What is zero times infinity?

Question

If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? Do they cancel one another out and equal any number since any number = 0 to infinity) and any number infinity to 0? "also can 0 and infinity be one an others inverse?

Answer 1

Since infinity is a concept and not a number, you can't use it as a number in arithmetic. However, I invite you to ponder these questions:

1. As $x$ becomes infinitely large, the function $x^2$ increases to infinity, but the function $\frac{1}{x^2}$ gets closer and closer to zero. What is $(x^2)(\frac{1}{x^2})$ equal to as $x$ becomes infinitely large?

2. The same can be said of $x^4$ and $\frac{1}{x^3}$. However, what is $(x^4)(\frac{1}{x^3})$ equal to as $x$ becomes infinitely large?

3. What is $(x^3)(\frac{1}{x^4})$ as $x$ becomes infinitely large?

4. What is $(0)(x)$ as $x$ becomes infinitely large?