Number agreement for negation and “or”

Which is correct/preferred:

There is no such thing as a base -1 or base 0 number representation.

There are no such things as base -1 or base 0 number representations.

There is no such thing as base -1 or base 0 number representation.

For the intended audience, "base x number representation" is a term of art, so both "There is no such thing as base -1 number representation" and "There is no such thing as a base -1 number representation" (with the indefinite article "a") would be used, with the former perhaps being more common.

• Pick the first. – Lawrence Sep 19 '17 at 18:30
• (there's no base 1 either) – AmI Sep 19 '17 at 18:57
• @AmI - Sure there is. It's also called the unary numeral system. Pick a symbol (say, "1") and represent a natural number n by repeating the symbol n times. It fits in nicely with the other place-value systems because every place has value 1 (since 1^i = 1 for every i). – Ted Hopp Sep 19 '17 at 19:01
• But it doesn't fit in perfectly -- unary should not be equated with base 1. – AmI Sep 19 '17 at 19:08
• @AmI - In theory you are right. However, pretty much everyone does equate the two (including the Wikipedia article I linked to). It is a special case, of course, since there's no 0 and, because there's no scaling, no meaning to a decimal point. That's why it's only usable for representing natural numbers. – Ted Hopp Sep 19 '17 at 19:22