Why does every string contain the empty string?

Question

"ABCDE" has no empty character. But when I type ``` "" in "ABCDE" ``` Python interpreter returns `True`. Why? is there any empty character in "ABCDE"? I don't think so. And I also found when I use these code: ``` target = '' src = 'ABCDE' src.find(target) ``` it returns 0 instead of -1 Why is this?

Accepted Answer

For people with background in languages where string objects represented as arrays of characters it may be surprising, but if we try to follow such approach like

```
string = 'ABCDE'
characters_list = list(string)
```

then

```
'' in characters_list
```

will be `False` statement.

Empty string probably came from mathematics, where it is a neutral element for binary operation of string concatenation, i. e. for every string `a`

```
a + empty_string == empty_string + a == a
```

where `+` is a string concatenation symbol. Then "substringing" can be defined as follows:

for every strings `a`, `b` we say `a` is substring of `b` iff exists strings `c`, `d` such that

```
b == c + a + d
```

Let's denote `a` is substring of `b` as `a in b`.

With these definitions of empty string and substringing relation can be proved lemma

`empty_string` is a substring of any string `a`:

```
a == (definition of empty_string) == empty_string + a == 
== (definition of empty_string) == empty_string + empty_string + a
```

then if we define `c = empty_string` and `d = a`:

```
a == c + empty_string + d
```

and by definition `empty_string in a`.

Why does every string contain the empty string?

Solution

Problem