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... 2.2.1 (b) sup(S) = ∞, inf(S) = 0. (c) sup(S) = ∞, inf(S) = −∞. 2.2.3 (a) Let α = sup(S) for convenience. Notice that for every s ∈ S, s ≤ α, and so since a > 0, as ≤ aα. So, aα is an upper bound for aS. Now suppose b < aα. Then ab < α, and so ab is not an upper bound for S. Therefore there exists an ...
... 2.2.1 (b) sup(S) = ∞, inf(S) = 0. (c) sup(S) = ∞, inf(S) = −∞. 2.2.3 (a) Let α = sup(S) for convenience. Notice that for every s ∈ S, s ≤ α, and so since a > 0, as ≤ aα. So, aα is an upper bound for aS. Now suppose b < aα. Then ab < α, and so ab is not an upper bound for S. Therefore there exists an ...
Real Numbers, Exponents, and Scientific Notation
... to create mathematical models to help them understand the dynamics of systems from stars and planets to black holes. If you are interested in a career as an astronomer, you should study the following mathematical subjects: ...
... to create mathematical models to help them understand the dynamics of systems from stars and planets to black holes. If you are interested in a career as an astronomer, you should study the following mathematical subjects: ...
