Lecture 15

8 Outubro 2025, 11:30 • Alexandra Symeonides

Sublimits of sequences that admit a limit, even and odd subsequences.
Upper and lower limits. Limit versus upper and lower limits.
Exercises discussed with the students ex. 4.6.4 iv) 4.6. 5 b) c) e).

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Lecture 14

8 Outubro 2025, 10:00 • Alexandra Symeonides

Comparison theorems for limits.
Subsequences, Bolzano-Weierstrass theorem.
Definition of sub-limits and sub-limits of unbounded sequences.

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Lecture 13

6 Outubro 2025, 11:30 • Alexandra Symeonides

Numerical Sequences

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Lecture 12

1 Outubro 2025, 11:30 • Alexandra Symeonides

Open Closed and Compact sets
ex 3.3.6. A_1 b) and A_2, 3.3.8, 3.3.10, 3.3 13

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Lecture 11

1 Outubro 2025, 10:00 • Alexandra Symeonides

Accumulation points and derived set. 
Characterization of accumulation points
ex. 3.3.6 A_1 a)

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