Description:
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Table 1 in the documentation on the "syslog" function says "syslog() Priorities (in descending order)". The table starts with LOG_EMERG, which is defined as 0 (zero).

As is always the case with priority lists, one is easily misunderstood. If A has a higher priority than B, it means in this case A < B.

Suggested solution:
1) Place the values of the constants in the table explicitly.
2) or put an example in that shows how to compare priorities.