In supply-and-demand curve, we draw curves of indifference. Say the demand goes through (1, \$1). Then Bob the Buyer is indifferent between spending \$1 for 1 apple or just keeping the \$1. If Sally the Seller had 1 apple to sell, then the equilibrium quantity sold would be 0 or 1—we cannot say. Seen differently, Bob will buy 1 apple if the price is in the interval [\$0, \$1) (and he may buy it if the price is exactly $1).
Would it not be simpler to use closed intervals? In our example, Bob will buy 1 apple is the price is in the interval [\$0, \$1]. The equilibrium quantity sold will definitely be \$0. Seen differently, the demand curve represents the maximum price buyers will pay, and the supply curve represents the minimum sellers will sell for.
It's (literally) an infitesmal of a difference, but it seems, at least for discrete situations like the above, it would be nice to say exactly what will happen.
Why don't we do that? There must be some elegant reason.