MySQL: Auto increment temporary column in select statement

Question

How do I create and auto increment a temporary column in my select statement with MySQL?

Here is what I have so far:

SET @cnt = 0;
SELECT
    (@cnt =@cnt + 1) AS rowNumber,
    rowID
FROM myTable
WHERE CategoryID = 1

Which returns:

+++++++++++++++++++++
+ rowNumber | rowID +
+++++++++++++++++++++
+  (NULL)   |   1   +
+  (NULL)   |   25  +
+  (NULL)   |   33  +
+  (NULL)   |   150 +
+  (NULL)   |   219 +
+++++++++++++++++++++

But I need:

+++++++++++++++++++++
+ rowNumber | rowID +
+++++++++++++++++++++
+  1        |   1   +
+  2        |   25  +
+  3        |   33  +
+  4        |   150 +
+  ...      |   ... +
+++++++++++++++++++++

Answer 1

This will give you a consecutive row number with 3.

SELECT
    (@cnt := @cnt + 1) AS rowNumber,
    t.rowID
FROM myTable AS t
  CROSS JOIN (SELECT @cnt := 0) AS dummy
WHERE t.CategoryID = 1
ORDER BY t.rowID ;

Result

| ROWNUMBER | ROWID |
---------------------
|         1 |     1 |
|         2 |    25 |
|         3 |    33 |
|         4 |   150 |