Other that Infinity itself, of course.
The shortest I've found is 1e309.
(This is essentially a rehash of: Is there is a more concise representation of Infinity in JSON than 1e309?)
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1Not shorter, but smaller: 2e308 – Rick Regan Jan 29 '16 at 20:15
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Hmm. Along those lines, the smallest might begin with 9 – Andrea Jan 31 '16 at 01:21
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Do you think that beginning with a `9` is going to be sufficient to save a digit on the exponent? – Pascal Cuoq Jan 31 '16 at 05:30