When a = b and a != b both return true...

In XPath = and != are set operators. That is, they return true if any item on the left hand side returns true when compared with any item on the right hand side. Or in other words:

some x in $seqA, y in $seqB satisfies x op y

...where "op" is = or != (or > or < etc)

To demonstrate this take the two sets ('a', 'b') and ('b', 'c'):

$seqA = $seqB returns true because both sets contains 'b'

$seqA != $seqB returns true because setA contains 'a' which is not equal to 'c' in setB

This catches me out a lot, even though I've been caught out before several times. I really have to think hard about what it is exactly that I'm comparing, and still end up getting it wrong.

A simple rules to follow is "never use != where both sides are sequences of more than one item". 99.9% of the time you won't need to, as much as it feels like the right thing to do.

Below are some of the most common operations on sequences, put together for a reference.

The two sequences are ('a', 'b') and ('b', 'c'), which can be defined in XSLT as:

<xsl:variable name="seqA" select="('a', 'b')" as="xs:string+"/>
<xsl:variable name="seqB" select="('b', 'c')" as="xs:string+"/>

or in XQuery as:

let $seqA := ('a', 'b')
let $seqB := ('b', 'c')

Select all items in both sequences

($seqA, $seqB)

Result: a b b c

Select all items in both sequences, eliminating duplicates

distinct-values(($seqA, $seqB))

Result: a b c

Select all items that occur in $seq1 but not $seq2

$seqA[not(. = $seqB)]

Result: a

Select all items that occur in both sequences

$seqA[. = $seqB]

Result: b

Select all items that do not occur in both sequences

($seqA[not(. = $seqB)],$seqB[not(. = $seqA)])

or

($seqA, $seqB)[not(. = $seqA[. = $seqB])]

Result: a c

Determine if both sequences are identical

deep-equal($seqA, $seqB)

Result: false

Test if all items in the sequence are different

count(distinct-values($seqA)) eq count($seqA)

Result: true