Why is infinity times 0 indeterminate

However, infinity is not a real number. It means something approaching infinity multiplied by something approaching zero. And this doesn't have to be zero at all. Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form. Your title says something else than "infinity times zero".

It says "infinity to the zeroth power". But there is no universal rule: the result will depend on the functions. Zero is also the winner in your particular homework problem. About the only thing you can say with certainty is that the result won't be negative if the factors are positive a 'positive indeterminate' if you like.

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Learn more. Ask Question. Asked 10 years, 5 months ago. Active 10 years, 5 months ago. Viewed 6k times. Add a comment. Active Oldest Votes. MartianInvader MartianInvader 5, 16 16 silver badges 31 31 bronze badges. Which, in retrospect, isn't exactly the same. Thanks for your help. I hope you don't take this personally. Such a rule applies whether or not fractional powers would make sense e.

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