It depends. The determining factor is whether the numerator goes to infinity faster or slower than the denominator. If the numerator goes faster, then the answer is infinity. For example, as x goes to infinity, exp(x)/x goes to infinity. If the numerator goes slower, then the answer is zero. For example, as x goes to infinity, x/exp(x) goes to zero. If they go at the same rate, then the answer is intermediate. For example, 2x/x is 2 for all x, including when x goes to infinity.
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The answer to this whimsical but useless exercise is: Infinity
To express the idea of infinity.
Zero times infinity is defined as "indeterminate".
infinite
A good sentence for infinity: A concept for a value that increases or decreases without bound is known as infinity.