Dictionaries tend to use popular definitions rather than accurate definitions. The reason is not enough people care. So decimate now means the opposite of what it used to mean. It used to mean when an army lost a battle the soldiers would be punished. One in ten would be killed!
Dictionaries are supposed to use popular definitions, that is their purpose, to document the current and common usage of each word. Even a math dictionary, which is restricted to just one domain (mathematics) suffers the same fate of change in word usage. While looking at textbooks published 100 years ago, the terms "involution" and "evolution" were used to describe the operations of raising to a power or taking the root.
I use a bit more in my definitions than what I wrote. For example "Addition is an operation on two numbers, called the "addends" which produces a result called the "sum" or "total". It is the inverse of subtraction.
I don't start with that though, in fact at the very beginning of addition I don't start with a definition at all, the kids are too young. I start by just showing the operation and pointing to the elements and naming them. I think children are unable to use a dictionary till the 3rd grade or so. It is something (the ability to use a dictionary) that you have to build up to.
You bring up a good point though. Some students are more pedantic than others. I do think a student must establish a good sense of formality (and we should help that) but at the same time I don't want them hindered by it. I want them to be able to improvise. Jazz musicians for example, have great music theory, but they also have great feeling. In mathematics I want both theory and feeling as well.