Let $S$ Be the Set of All Strings in 0's and 1's

question 17

Essay

Let $S$ be the set of all strings in 0's and 1's, and define a function $g$ : $S \longrightarrow \mathbf { Z }$ as follows: for each string $s$ in $S$ ,
$g ( s ) =$ the number of 1's in $s$ minus the number of 0 's in $s .$
(a) What is $g ( 101011 ) ? g ( 00100 )$ ?
(b) Is $g$ one-to-one? Prove or give a counterexample.
(c) Is $g$ onto? Prove or give a counterexample.

---

Definitions:

Esse Est Percipi

A Latin phrase meaning "to be is to be perceived," associated with George Berkeley's idealist philosophy which argues that objects only exist to the extent that they are perceived.

Subjective Idealism

The view that nothing exists except ideas and minds. The eighteenth-century idealist George Berkeley held the extreme position of subjective idealism, which, simply summarized, insisted that “to be is to be perceived” (esse est percipi). According to Berkeley, it makes no sense to believe in the existence of anything that we cannot experience.

Western Metaphysical Tradition

A lineage of philosophical inquiry in the West that deals with fundamental questions of existence, reality, and knowledge.

Most Real

This term is likely to refer to the philosophical notion of ultimate reality or truth, the most fundamental and true nature of existence as opposed to appearances or perceptions.