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Consider the function ?:[0,1] → ℝ defined by ?(?) = 0 if ? ∈ [0,1] ∖...

Consider the function ?:[0,1] → ℝ defined by ?(?) = 0 if ? ∈ [0,1] ∖ ℚ and ?(?) = 1/? if ? = ?/? in lowest terms

1. Prove that ? is discontinuous at every ? ∈ ℚ ∩ [0,1].

2. Prove that ? is continuous at every ? ∈ [0,1] ∖ ℚ

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