If I think about it some more, why not get rid of all the float
platform-dependencies and define how +inf, -inf and nan behave?

I think that it means:
* inf and -inf are legitimate floats just like any other float.
Perhaps there should be a builtin Inf, or at least math.inf.
* nan is an object of type float, which behaves like None, that is:
"nan == nan" is true, but "nan < nan" and "nan < 3" will raise an
exception. Mathematical operations which used to return nan will raise
an exception (division by zero does this already, but "inf + -inf"
will do that too, instead of returning nan.) Again, there should be a
builtin NaN, or math.nan. The reason for having a special nan object
is compatibility with IEEE floats - I want to be able to pass around
IEEE floats easily even if they happen to be nan.

This is basically what Tcl did, if I understand correctly - see item 6
in http://www.tcl.tk/cgi-bin/tct/tip/132.html .