Re: order on the sets

Consider an order on the interval such that
[a,b] is higher than [c,d] iff b=>c.

If you ask that [a,b] <= [c,d] iff b<=c, then
you get a particular class of partially ordered
set called a semi-order.

Is [a,b] <= [r,s] when b <= r is an (partial) order
for { [a,b] | a <= b }?

... it's not reflexive.

However [a,b] < [r,s] when b < r is an irreflexive
order.

My apologies - I mis-spoke myself. I intended to
say [a,b]<[c,d] iff b<c, and to use the irreflexive
formulation of partial and semi-orders. Thank you
for your highlighting of the details.
.