Does PostgreSQL numeric type support infinity (and -infinity)?

NUMERIC does not support +-infinity, though it does support NaN. That's rather an unfortunate limitation. Addressing it would probably require changing the on-disk binary format of numeric which could be challenging...

craig=> SELECT NUMERIC 'NaN';
 numeric 
---------
     NaN
(1 row)

craig=> SELECT NUMERIC '-inf';
ERROR:  invalid input syntax for type numeric: "-inf"
LINE 1: SELECT NUMERIC '-inf';
                       ^
craig=> SELECT NUMERIC '+inf';
ERROR:  invalid input syntax for type numeric: "+inf"
LINE 1: SELECT NUMERIC '+inf';

craig=> SELECT NUMERIC '+infinity';
ERROR:  invalid input syntax for type numeric: "+infinity"
LINE 1: SELECT NUMERIC '+infinity';
                       ^
craig=> SELECT NUMERIC 'infinity';
ERROR:  invalid input syntax for type numeric: "infinity"
LINE 1: SELECT NUMERIC 'infinity';
                       ^
craig=> SELECT NUMERIC '-infinity';
ERROR:  invalid input syntax for type numeric: "-infinity"
LINE 1: SELECT NUMERIC '-infinity';

PostgreSQL will support numeric +inf/-inf from v14