Please explain "set difference" in Python

Question

Trying to learn Python I encountered the following:

>>> set('spam') - set('ham')
set(['p', 's'])

Why is it set(['p', 's']) - i mean: why is 'h' missing?

• Martijn Pieters: Why do you expect h to be included?
• Rockbot: I thought it is to show the differences, so from my feeling I expected h to be included. Looks like I got the concept wrong.

Answer 1

The - operator on Python sets is mapped to the difference method, which is defined as the members of set A which are not members of set B. So in this case, the members of "spam" which are not in "ham"are "s" and "p". Notice that this method is not commutative (that is, a - b == b - a is not always true).

You may be looking for the symmetric_difference or ^ method:

>>> set("spam") ^ set("ham")
{'h', 'p', 's'} 

This operator is commutative.

• NPE: I believe the statement [The ^ operator] corresponds more to the mathematical notion of set difference is misleading. It does correspond to the mathematical notion of symmetric difference, but not to the mathematical notion of set difference.
• jjm: Ah, you're correct. The mathematical notion of set difference, according to wolfram, is actually the - operator.

Answer 2

Because that is the definition of a set difference. In plain English, it is equivalent to "what elements are in A that are not also in B?".

Note the reverse behavior makes this more obvious

>>> set('spam') - set('ham')
{'s', 'p'}
>>> set('ham') - set('spam')
{'h'}

To get all unique elements, disregarding the order in which you ask, you can use symmetric_difference

>>> set('spam').symmetric_difference(set('ham'))
{'s', 'h', 'p'}

• Jon Clements: You don't need set('ham') here - set methods take any iterable, so using set('spam').symmetric_difference('ham') is fine

Answer 3

There are two different operators:

• Set difference. This is defined as the elements of A not present in B, and is written as A - B or A.difference(B).
• Symmetric set difference. This is defined as the elements of either set not present in the other set, and is written as A ^ B or A.symmetric_difference(B).

Your code is using the former, whereas you seem to be expecting the latter.

Answer 4

The set difference is the set of all characters in the first set that are not in the second set. 'p' and 's' appear in the first set but not in the second, so they are in the set difference. 'h' does not appear in the first set, so it is not in the set difference (regardless of whether or not it is in the first set).

Answer 5

You can also obtain the desired result as:

>>> (set('spam') | set('ham')) - (set('spam') & set('ham'))
set(['p', 's', 'h'])

Create union using | and intersection using & and then do the set difference, i.e. differences between all elements and common elements.