What is zero times infinity?

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  • Why is Infinity multiplied by Zero not an easy Zero answer?

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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?