Definition talk:Prime Decomposition/Multiplicity

I'm against the merge for the reason that the language it uses is immediately accessible at an elementary level. It is more or less directly clear what it means: it's the number of times you can divide an integer by one of its prime factors.

The definition of the $p$-adic valuation, while it means exactly the same thing, requires awareness of more specialised language and notation that you don't get until undergraduate level, and it obscures the meaning unless you are completely familiar with it -- and even then when you get the meaning it's "Oh yes of course, it's the number of times you can divide an integer by one of its prime factors."

It is important that whatever we do here, we retain the immediacy of what this definition really means.

Maybe there's a case for writing a page interpreting it at an even simpler level than either of the definitions we have here. --prime mover (talk) 02:19, 28 April 2020 (EDT)