Speaking of mathematical missteps relating to bases, I've always been baffled by why we refer to a base system by the number above the highest representable single digit. Every base is "base 10" in that case! Why is binary referred to as "base 2", when the number 2 doesn't even appear? Wouldn't it make infinitely more sense to refer to our conventional number system as "base 9", binary as "base 1", unary as "base 0", and hexadecimal as "base F"? Or we could have used a more sensical word like "ceiling" or "roof" in that case, to convey that it's referring to the highest single-digit value in the system.