Mathematical mumbo-jumbo

What is a “p-adic valuation?”

What is the meaning of $\operatorname{ord}_{p}(n)$?
In number theory, where $p$ is a prime number and $n$ is an integer not equal to zero, what is the definition of the function $\operatorname{ord}_{p}(n)$ in the context of $p$-adic valuations?

These mathematicians need to clean up their language. It sounds altogether too much like an atrocious bill from a pædiatric clinic for a large amount of money, and just a little bit too prim and proper with it, to boot.

I was once a kid with an avid interest in mathematics. You can write down an equation, it is whatever it is, but use real English words. Explain what you mean. Don’t talk that sick twisted criminal cant jargon around kids.