Table R3.1 gives an overview of the properties of operations on numbers in the different number systems. You could also ask your students to fill in the ‘yes’ and ‘no’.
Property of operations on numbers | Number system | |||||
---|---|---|---|---|---|---|
Natural | Whole | Integers | Rational | Irrational | Real | |
Closed under addition: If a, b belong to a set, then a + b also belongs to the set. | Yes | Yes | Yes | Yes | No | Yes |
Additive identity: For a belonging to a set, there is a number z in the set, such that a + z = a. | No | Yes | Yes | Yes | No | Yes |
Additive inverse: For every number a in a set, there is another number –a in the set such that, a + (–a) = z. | No | No | Yes | Yes | No | Yes |
Closed under multiplication: If a, b belong to a set, then a × b also belongs to the set. | Yes | Yes | Yes | Yes | No | Yes |
Multiplicative identity: For a belonging to a set, there is a number u in the set, such that a × u = a. | Yes | Yes | Yes | Yes | No | Yes |
Multiplicative inverse: For every number a in a set, there is another number a-1 in the set such that, a x a-1 = u | No | No | No | Yes | No | Yes |
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