Why Read This Book? - Index of

Solution We show that T satisfies properties F1–F2.
4.1 Definition and Examples 123
(F1) Pick x ∈ Nn. Since 1 ≤ x ≤ n, it follows that 1 + m ≤ x + m ≤ n + m, or
1 + m ≤ T(x) ≤ n + m. Thus T(x) ∈ Nm n .
(F2) Pick x1,x2 ∈ Nn and suppose x1 = x2. Then since addition is well defined,
T(x1) = x1 + m = x2 + m = T(x2). Thus T is well defined. �
Notice that showing F1 in Example 4.1.5 involves not only showing that T(x) exists,
but that it lies in the codomain.
If a and b are real numbers such that aa}
(−∞,b]={x ∈ R : x ≤ b}
(−∞,b)={x ∈ R : x