XSD datatype

xs:positiveInteger

An integer of 1 or more. Zero is not positive, which is the distinction from xs:nonNegativeInteger.

xs:positiveInteger has minInclusive fixed at 1; xs:nonNegativeInteger has it at 0. The difference is exactly whether zero is allowed, and choosing the wrong one is a common schema bug — a quantity of 0 is usually meaningful, a quantity of −1 is not.

Both are unbounded above, because both derive from xs:integer.

Lexical space: Optional plus sign, then digits, with a value of 1 or greater.
Derives from: xs:nonNegativeInteger
Category: Numeric types
Facets: minInclusive, maxInclusive, minExclusive, maxExclusive, pattern, enumeration, whiteSpace, totalDigits, fractionDigits

What validates

Every literal below is put through the schema validator on each test run, against the schema at the foot of this page.

1
+1
999999999999999999999

What does not

0
Zero is not positive.
-1
Negative values are excluded.
1.0
No decimal point.

What catches people out

Zero fails. If a count of zero is legitimate, xs:nonNegativeInteger is the type you meant.
Still unbounded above — 'positive' constrains only the lower end.

The schema used

This is the exact schema the literals above are validated against. Paste it into the validator with one of them to see the result yourself.

schema.xsd

<?xml version="1.0" encoding="UTF-8"?>
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema">
  <xs:element name="v" type="xs:positiveInteger"/>
</xs:schema>

Open the XSD validator