I found a couple of answers online but I don't quite understand why the answer is right:

  1. The length of a string is:
    If a string has no characters, then its length is 0.
    Otherwise, the length of the string is 1 + length of the tail

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  • 2
    $\begingroup$ Don't use images as main content of your post. This makes your question impossible to search and inaccessible to the visually impaired; we don't like that. Please transcribe text and mathematics (note that you can use LaTeX) and don't forget to give proper attribution to your sources! $\endgroup$
    – dkaeae
    Apr 29 '19 at 18:47

Strings are concatenations of characters. Hence, any non-empty string $w$ has a first character $x$ and can be written as $w = x w'$, where $w'$ is the tail string. It follows from the definition of a string's length that $|w| = |x w'| = |x| + |w'| = 1 + |w'|$.


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