How can SQL test for pure numerics?

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If it's a numeric datatype column, you don't have to test it at all. <grin>

So the question of how to test for pure numerics is relevant only to string datatype columns, like CHAR and VARCHAR. And the specific method is pretty much dictated by whatever functions may be available in your particular DBMS.

In DBMSs which have one, like SQL Server, use the ISNUMERIC() function. In MySQL and PostgreSQL, use a regular expression such as '^[0-9.]$'. Note that the decimal point should be considered one of the valid "numeric" characters.