Analysis · Number
Sequences and Convergence
A sequence converges if for every ε > 0 there exists N such that all subsequent terms are within ε of the limit. Bolzano-Weierstrass: every bounded sequence has a convergent subsequence.
WHAT STUDENTS WILL LEARN
✓Define convergence using ε-N
✓Prove convergence from the definition
✓Apply Monotone Convergence and Bolzano-Weierstrass
✓Prove the Cauchy criterion
BUILDS ON
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