Let me quibble.

> * Float and Double are imprecise types by their very nature. That's exactly 
> what people are forgetting, and exactly what's causing misunderstandings. 

Float and Double are precise types. What is imprecise is the correspondence 
between finite precision floating point types (which are common to all 
programming languages) and the mathematical real numbers. This imprecision is 
manifest in failures of the intended homomorphism from the reals to the 
floating point types.

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