If zero times anything is zero, and infinity times anything is infinity, then what is zero times infinity?
In: Mathematics
It’s not defined.
There’s also the question of “what infinity”, but in this particular case, almost all reasonable ideas of trying to multiply those two together yield “not defined”.
There is one exception that I know of. In measure theory, you usually kinda take zero times (countable) infinity to be 0. The idea there kinda is that, measure theory tries to be a way to discuss all different “measures”, like length, area, volume, etc, and adding together stuff, with zero length for example, gives you end result that’s also zero length. This works up until countable infinity. Beyond that, it no longer works(for example, a line consists of uncountably many points of zero length. That should tell you that uncountably many of zero lengths breaks down this arithmetic)
But “not defined” is the safest answer. The reason being in the title, if infinity times anything is infinity, and zero times anything is zero, and zero ain’t infinity, zero times infinity can’t be defined. But as always in math, you gotta understand the context. Sometimes multiplying zero by infinity makes sense. Admittedly it’s rare, though
Latest Answers