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Blast into Math! ets of nummers: mathematical plaagrounds

3.5 Exercises

1. Verify by looking up mathematical publications from authors around the world that the
symbol Z is used by Asian, European, Australian, African, and American mathematicians
alike.
2. Let’s introduce some new notation:
a := b,

means: a is defined to be equal to b. Prove that for a non-empty set X ⊂ Q which is bounded
above, its twin

Y := {−x ∈ Q such that x ∈ X}

is bounded below, and if L is the LUB of X , then −L is the GLB of Y .

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