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remembered "real induction" just earlier https://t.co/6iGYOT6mSo let A ⊆ [a, c). if - there is b₀ s.t. [a, b₀) ⊆ A - whenever [a, b) ⊆ A, there is b' > b s.t. [a, b') ⊆ A then we have A = [a, c) look @ this proof that closed intervals are compact! htt