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There is a simple problem, and I gave my simple prove. Could anybody help me check whether it is correct:

Show that if B is not finite and [tex]{B}\subset{A}[/tex], then A is not finite.

My prove:

Since B is not finite, there exists a bijection of B into one of its proper subset, C, say, and denote the function to be f: [tex]{B}\rightarrow{C}[/tex].

Since B is a proper subset of A, as an extension of f to A,there exist a (some) bijiection(s), say g, such that g: [tex]{A}\rightarrow{C}[/tex]. And thus g maps A onto its proper subset, A cannot be finite. Hense A is infinite.

Thks!

Show that if B is not finite and [tex]{B}\subset{A}[/tex], then A is not finite.

My prove:

Since B is not finite, there exists a bijection of B into one of its proper subset, C, say, and denote the function to be f: [tex]{B}\rightarrow{C}[/tex].

Since B is a proper subset of A, as an extension of f to A,there exist a (some) bijiection(s), say g, such that g: [tex]{A}\rightarrow{C}[/tex]. And thus g maps A onto its proper subset, A cannot be finite. Hense A is infinite.

Thks!

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