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What is 1 / infinity? Is it even possible to divide by infinity?

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- #1

member 529879

What is 1 / infinity? Is it even possible to divide by infinity?

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Mark44

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No, and you can't use ∞ in arithmetic expressions.What is 1 / infinity? Is it even possible to divide by infinity?

Where expressions such as this often show up is in limit expressions, such as ##\lim_{x \to \infty} \frac{1}{x}##. The value of this limit is 0. We don't write 1/∞.

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One of the problems with allowing these undefined quantities to be used as though they were numbers is that by using them you can readily prove that any number is the same as any other number.

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Like this? :)

1+2+3... the partial sums of the infinite series grow without bound = infinity

1+2+3...can be summed to equal -1/12

if two things equal to the same thing are themselves equal

then

1/infinity = 1/(-1/12) = -12

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