User talk:Andyk 94
I've found some Wikipedia pages that can help
[edit]I've found these two pages:
The first addresses the issue directly, explaining how mathematicians use this terminology. The second explicitly says there are "arbitrarily long, but not infinitely long" arithmetic progressions of prime numbers.
To say that there are arbitrarily long arithmetic progressions of prime numbers DOES NOT mean that there is any particular arithmetic progression of prime numbers that is "arbitrarily long". There is no such thing. It means that no matter what length you pick, no matter how big, there are arithmetic progressions that are at least that long (but still may be finite, and in this case are always finite).
The same thing applies to the phrase "arbitrarily small".
That's just part of the standard jargon of mathematicians. Michael Hardy (talk) 21:20, 19 July 2008 (UTC)