Continuity and uniform continuity
General · Mathematics
Study notes
Q: Is f(x) = 1/x uniformly continuous on (0,1)? On [1,∞)? On (0,1): NO! Near 0, tiny x-changes → huge y-changes; δ must shrink with location! On [1,∞): YES: |1/x-1/y| = |x-y|/(xy) ≤ |x-y| (xy ≥ 1): δ = ε works everywhere! Uniform: ONE δ for all points (global control!)!