Question

A ballpoint pen, also known as a biro,[1] or ball pen, is a pen that dispenses ink over a metal ball at its point, i.e. over a "ball point". The metal commonly used is steel, brass, or tungsten carbide.[from Wikipedia]
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According to the definition,can we use 'ball pen'?
1. I have a ball pen.
2. I wrote a letter with a ball pen.
3. I have two ball pens.
(Are thes sentences grammatical?)

Answer 1

They're usually referred to as 'ball point pens.'

Substitute 'ball point' for 'ball' in your sentences, and they'll be fine.