Why is a unary numeral system bijective?

Question

In this treatment of unary numeral system, it is called "bijective base-1 numeral system." I understand bijective from functions, but why is it used here? Also, the article says the Peano as well as Church numbers are unary numeral systems. Peano's system is based on repeating a successor function. Yes, I suppose a Peano number resembles tally marks. Basically, I'm not understanding the use of unary nor bijective here.

Answer 1

Unary simply means it is a base-1 notational system (only one digit), as opposed to binary (2 digits, "0" and "1), or decimal (10 digits, "0" … "9").

The pop-up note on "bijective" in the linked article says:

Bijective numeration is any numeral system in which every non-negative integer can be represented in exactly one way using a finite string of digits.

For instance the value 4 can be represented as "1111", and only as "1111"; and similarly the representation "1111" matches the value 4 and only the value 4.

That property holds for all values, and makes it bijective.