On Saturday, 26 July 2014 at 16:43:06 UTC, Fool wrote:
NaN < x is false
NaN > x is false
...which means that < as it is usually defined on floating
point numbers does not define a strict weak ordering.
Are you sure?
Properties of a Strict Weak Ordering:
#1 not(a < a)
#2 not(a < b and b < c) or a < c
#3 not(a < b) or (not b < a)
#4 not(a < b) or (a < c or c < b or ( a < c and c < b))
#1 is always true
#2 is always true if any of a,b,c are NaN
#3 and #4 are always true if any of a,b are NaN by "not(a<b)"
if you try to derive equality from that you would get:
NaN == x is true
This is not a contradiction to what I wrote.
Maybe you are right, but it does not match up to what I arrived
at based on the properties for Strict Weak Ordering listed in
Wikipedia.
