2.3 Float IEEE 7540-2008 or RFC7159 - STIX Part 1

2.3 Float reads in part:

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The float data type represents an IEEE 754 [IEEE 754-2008] double-precision number (e.g., a number with a fractional part). However, because the values ±Infinity and NaN are not representable in JSON, they are not valid values in STIX.

In the JSON MTI serialization, floating point values are represented by the JSON number type [RFC7159].
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OK, since you can only represent a subpart of IEEE 754, why not simply start with the floating point definition of JSON? Don't worry about subsetting IEEE 754. Yes?