numeric and float comparison oddities

I saw some strange results:

postgres=# select '1.1'::numeric = '1.1'::float8;
?column?
----------
t
(1 row)

postgres=# select '1.1'::numeric = '1.1'::float4;
?column?
----------
f
(1 row)

When I looked into it, I saw that the numeric is being cast to a float8,
making the first statement trivially true.

Why does the cast go from numeric to float if that direction loses
precision? One reason is because float supports +/- infinity, but that
seems more like convenience than a good reason. Is there another reason?

Have we considered adding +/- infinity to numeric so that it can
represent every float value? That might make the numeric hierarchy a
little cleaner and less surprising.

Regards,
Jeff Davis