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August 4, 2022

Using the Archimedean Property to prove convergence.

The Midterm will cover sections 1.1 — 2.3.

Some possible topics for the Midterm:

(1) Rational and irrational numbers and their properties.

(2) Proof by contradiction.

(3) Completeness Axiom.

(4) Archimedean Property. Using the Archimedean Property to find the Infimum and Supremum of bounded sets.

(5) Triangle inequality.

(6) Convergence of sequences. The epsilon-N definition of convergence.

(7) Using the Archimedean Property to prove convergence.

(8) Monotone sequences. Monotone Convergence Theorem.
(9) Application of the Monotone Convergence Theorem to series with nonnegative terms.

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