Question: 1. Consider the set P = {x R : x = a+ b 3+c 7+d 21}, in terms of arithmetic properties is P more like

1.

Consider the set P = {x R : x = a+ b 3+c 7+d 21}, in terms of arithmetic properties is P more like N, Z, or Q?

2.

Let S denote the set of rational numbers q such that

q <3

in lowest terms, the denominator of q is a power of two.

Prove that S does not have a maximum

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