If zero times anything is zero, and infinity times anything is infinity, then what is zero times infinity?
In: Mathematics
“Infinity” is not an element of the standard real number system, so if you want to say something like “infinity times anything is infinity”, you have to choose an alternate system of numbers that actually includes infinite values. There are several of these, which appear in different areas. Using the extended real numbers, which includes points +infinity and -infinity at either end of the real number line, 0 * +infinity and 0 * -infinity are simply undefined. Using the cardinal numbers of set theory, there are many different infinite values, but you still have x * 0 = 0 for any x, whether finite or infinite. As with anything in mathematics, you have to be precise about what you mean by “zero times infinity” before you can talk about it.
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