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A long time ago I got asked the product of every real number except 0. The person was looking for -1 and the first mapping I tried was a -> 1/a so i got the answer. never really thought about it again. Just realized that you could map a -> 1/(2a) and the answer would seem to be an infinite product of 1/2's. can someone find why this new map wouldn't cover every real number except 0? if it was right, this would imply that the product of every real number is both -1 and 0 and infinity (a -> 2a)

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# The product of every number

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