Unformatted text preview: Question 2 : Must f be onto? Answer 2: No. Counterexample : X = { 1 } , Y = ℝ ,Z = { 1 } . Define f: X ℝ by f x = 1 ∀ x ∈{ 1 } and define g: ℝ Z by g y = 1 ∀ y ∈ ℝ . Here g ° f x = 1, and g ° f: { 1 }{ 1 } is onto, but f: { 1 } ℝ is not onto....
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 Spring '08
 Ellis,W
 Logic, INFS

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