If zero times anything is zero, and infinity times anything is infinity, then what is zero times infinity?
In: Mathematics
An infinity times anything is not always an infinity.
An infinity times any finite number (other than zero) is always an infinity. Finite numbers are the normal numbers we normally deal with, one, ten, pi, square root of two, negatives, one divided by a trillion, they are all finite.
There are also infinitesimal numbers, numbers which are smaller than any finite number (other than zero). Any tiny little number you can think of, it’s larger than an infinitesimal: one-trillionth, one-trillionth of a trillionth, any of that sort, they are all larger than an infinitesimal.
These infinitesimal numbers have little practical use and so are not usually dealt with or talked about. They mostly serve to deal with infinities, and their most important feature is that an infinitesimal times an infinity is not an infinity.
Zero is even less than an infinitesimal, and an infinity times zero is always zero.
It should also be pointed out that an infinity is not a number, it is many number. An infinite number of numbers.
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