[Slightly OT]: More on ints and floats

[Lulu of the Lotus-Eaters]

|Floats are perfectly normal rational numbers; it's the *operations*
|which are weird.

Aren't you being slightly disingenuous here?

Any numbers are more-or-less only meaningful in terms of the operations
they enter into.  The Peano integers, or the Cauchy or Dedekind Reals,
are not really interesting because of the beauty of their construction,
but rather because it is relatively easy to define operations on them
that match our intuitions about how arithmetic is -supposed- to behave.
The operations are the whole point of the entities.

Likewise, a float isn't *really* a number at all.  It's really just a
pattern of bits, such as '01000001010000010100000101000001'.  Maybe
those bits are a way of representing the string "AAAA", or maybe they
are a way of representing a -thing- that enters into operations that act
(a little bit) like addition, multiplication, etc.  Just being a bit
pattern doesn't make it a *number* at all.

Yours, Lulu...

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