Hello:

Thank you for the kind words.

I think a discussion on the math terminology could be a great topic for a newsgroup. The short reply is that in the parts I came from my terminology is quite acceptable as long as it's consistent.

For most, the distinction you make or its purpose are next to incomprehensible while "integer" is a short word that resonates with even the innumerate.

I, for one, would never use "cardinal" in liew of "counting." "Cardinals" have been invented by Cantor and are usually (in my view) associated with a broader class of sets than finite. And the word "counting" itself, although pointing to the origin of arithmetic, is inappropriate when it comes to even such trivial results as Euclid's algorithm.

"Natural" numbers is an acceptable terminology. "Integer" has the advantage of being both an adjective and a noun thus allowing for shorter constructs.

Best regards,
Alexander Bogomolny

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