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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Analysis & Linear Algebra › The Real Line

“Every ordered field is Archimedean” — false

Counterexample locked — unlock with Notes + PYQ

real analysis

#2 · Analysis & Linear Algebra › Metric Spaces

“An arbitrary intersection of open sets is open” — false

Counterexample: ∩_{n≥1}(−1/n, 1/n) = {0}

Only finite intersections preserve openness.

topologyreal analysis