Borel Measurable and Borel Functions

Let f(x) be { 1/x if x is not 0. and 1 if x = 0} . Prove that f(x) is borel function ( borel measurable).

Borel measurability and Borel functions are investigated. The solution is detailed and well presented.

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Borel Measurable and Borel Functions - 1).Let f(X) : R -> R be the following: f(x) = { 1 if x is in Q (rationals) , 0 if x is not in Q ( irrational)} Prove that f(x) is Borel measurable ( Borel functions).
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