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

Answer 1

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.

Answer 2

Here's a qualitative way to think about it. Consider the following:

>>> "foo"[0:0]
''

Doing a zero-width slice of a string returns ''. So, if you can get '' out of a string, it must be in the string and therefore '' in "foo" must be true.