In mathematics, the expression "zero times infinity" is considered an indeterminate form, meaning it does not have a definitive value. This is because the product of zero and any finite number is zero, but the product of zero and an infinitely large number could potentially approach a non-zero value. In different contexts and mathematical systems, the result of zero times infinity may vary or be undefined.
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You cannt multiply by infinity in ordinary mathematics, because it is an undefined value.
However, for any other value, the result is zero. The intersection of a null (empty) set with other sets cannot exist, and in mathematics any value a x 0 = 0.
e.g. Zero times anything (even negative values) is always zero.
Infinity is undefined as a number, thus the definition of infinite.
However, as a concept, of an undefinable number, infinity is infinite, unending.
Infinity is not rational and keeps going on forever, therefore infinity cannot be multiplied by zero.
Multiplying infinity by other rational numbers is impossible in ordinary math, because the result cannot exceed infinity.
Any number over 0=∞. Frankly speaking, the answer is whatever the numerator was, or in algebra, n/0 x 0=n. The answer is undefined.
You can not divide by zero - it is not defined. Presumably you get infinity, but there are different types of infinity.
It remains as zero
If you tried to write out infinity, it would take an infinite amount of zeros. Seriously, infinity is unimaginably big, and then some - that's the point. It is absurdly huge. You think the national debt is big, but that's just peanuts compared to infinity.
When any number is multiplied by zero, the product is zero.
1 time infinity equals infinity. Infinite divided by infinite equals 1. There's your answer. * * * * * Except that it is not true. 1 times infinity is, indeed, infinity. But infinity divided by infinity need not be 1. See for example, the paradox of Hibert's Hotel at the attached link.