Infinity multiplied by any non-zero number (including infinity itself) results in infinity.
Here's a breakdown:
-
Infinity x Infinity = Infinity: When you multiply infinity by itself, the result is still infinity. Think of it as an unbounded quantity growing without limit even faster.
-
Infinity x Any Positive Number = Infinity: Multiplying infinity by any positive real number also results in infinity. For example, 2 * ∞ = ∞.
-
Infinity x Any Negative Number = Negative Infinity: Multiplying infinity by any negative real number results in negative infinity. For example, -2 * ∞ = -∞.
-
Zero x Infinity = Indeterminate: This is an indeterminate form, meaning it does not have a defined value. It can be thought of as approaching infinity from one direction while simultaneously approaching zero from another. The result could be anything depending on the specific context of the limit.
Therefore, the most direct answer to your question is:
Infinity multiplied by infinity equals infinity. Also, infinity multiplied by any non-zero real number equals infinity (or negative infinity if the number is negative).
