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But numerals "10" in bases other than decimal aren't usually called ten, I think.

"10" is never correctly called "ten" except in decimal. But this whole tangent is getting a little navel-gazey for me. "Base 10" is fine in my book because decimal is our inbuilt base.

That's what I said (or tried to :) ).

Should we call it "base a"?

"base ||||| |||||"

perhaps "base |||||*||", for short.

base II*II+II?

base X (romans)

Ten is "decem" in Latin. Decimal means, literally, base ten. It's a tautology either way. You can't even specify the base of the base since "base (10 in base 10)" presents the same problem recursively.

It's a non-problem though. I don't know about mathematicians, but when programmers say base N they mean N in decimal.

EDIT: woops, replied to the wrong post.

I get the parent poster's point, but to me it's like quibbling over people using "comprised of" instead of "comprises": some people will care, but in the grand scheme of things it's not a meaningful disagreement because everybody got what you were trying to say the first time, and there are only a few rare contexts where the distinction matters.

Base (((((((((1++)++)++)++)++)++)++)++)++)

Peano would be proud.