criterion
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Anything you like. You specify whatever rule you like and the resulting set of numbers is the sequence based on that rule.
An empirical rule indicates a probability distribution function for a variable which is based on repeated trials.
gentleness
Standard notation (in the UK) is the same as scientific notation. So the one rule to use is DO NOTHING!
The seniority rule functions by looking at the number of years one has been in an institution. This is an ideology that is based on hierarchical age.