Examples of maths laws being useful in software development

[JimmyHoffa]

Small explanation of the law in a math (function|operator), and a small code example of when such a law can be useful to have a code function meet

for instance: Small explanation of the law of associativity, and a snippet showing how having the null coalesce function associative gives you reliable chaining functionality; in JavaScript for instance:

var getPerson = function(personId) {
    return personRepo.get(personId, this.companyId) ||
           personRepo.get(personId) ||
           personRepo.getNewPersonTemplate();
}

repeat for laws of commutativity, reflexivity, transitivity, and any other maths laws that come to mind with perhaps a paragraph explaining why this law comes in handy for certain scenarios/what scenarios it comes in handy for