Let α, β be cuts as defined by the following: 1) α ≠ ∅ and α...

Let α, β be cuts as defined by the following:

1) α ≠ ∅ and α ≠ Q

2) if r ∈ α and s ∈ Q satisfies s < r, then s ∈ α.

3) if r ∈ α, then there exists s ∈ Q with s > r and s ∈ α.

Let α + β = {r + s | r ∈ α and s ∈ β}.

Show that the set of all cuts R with the addition defined above satisfies the axioms for addition (closed, associative, symmetric, identity, inverse)

Expert Solution

Colby Messinger answered 1 year ago

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