Signed-digit notation

We take signed-digit binary notation as our paradigmatic example. A signed-digit numeral is an infinite sequence over the signed-digit alphabet 40#40, where 7#7 stands for -1. As before, a numeral 41#41 denotes the number

42#42

and the surjection 29#29 is a quotient map 43#43. The above definitions and facts for standard numerals apply to signed-digit numerals, except that now one has that, in contrast to Proposition 6.4,

Proposition 7.1   Every continuous function 44#44 has a realizer 45#45 of finite character.

The same holds for functions of several arguments, with realizers defined in the obvious way.
46#46

Since one can effectively translate between the representations of real numbers discussed in Chapter 7, all of them have the same property.