Is (-inf or +inf) a good choice instead of `[-inf or +inf]` to express range info?

[wjhuang2016]

When excute desc select * from t;
We get

+-------------------+----------+------+------------------------------------------------------------+
| id                | count    | task | operator info                                              |
+-------------------+----------+------+------------------------------------------------------------+
| TableReader_5     | 10000.00 | root | data:TableScan_4                                           |
| └─TableScan_4     | 10000.00 | cop  | table:t, range:[-inf,+inf], keep order:false, stats:pseudo |
+-------------------+----------+------+------------------------------------------------------------+
2 rows in set (0.00 sec)

The range info here is [-inf,+inf], according to #9231 and #8588, we can improve it as [NULL,+inf) or (NULL,+inf) when explain select * from t use index(idx) where a is not null;

It seems that (-inf or +inf) is more reasonable than [-inf or +inf].
Should we use (-inf or +inf) even the scan is not a full range scan?

[eurekaka]

From the code perspective, NULL is "less" than -inf, if we adjust the display like your suggestion, when the range is full range with NULL, it would be like [NULL, +inf), and this implies that -inf is included in the range, which is inconsistent with the implication of (-inf, +inf)?

[wjhuang2016]

I got it. So we should use [NULL,+inf] to express a full range scan with NULL and (NULL,+inf] to express a full range scan without NULL?

[eurekaka]

I prefer [NULL, +inf] for full range, while [-inf, +inf] for full range without null. @zz-jason @winoros what's your opinions?

[winoros]

Another case is that the inf of some numeric type is an actual number not an unbounded limit.
For bigint type, +inf is 2^63-1 for signed. +inf] is the same with 2^63-1] and +inf) is the same with 2^63-1). There're some reasons that we cannot treat the +inf of some numeric type as an unbounded limit for now. So to not annoy our users, i prefer use [] for all types.