0 and 1 (and -1) are the only integers which are not prime nor composite. All non-integral numbers are also non-prime and non-composite. This is because the property is not defined for such numbers.
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The concept of "primes" and "composites" basically applies to integers larger than one. It doesn't apply to numbers in general; for example, it doesn't apply to:* Rational numbers
* Real numbers
* Complex numbers