- #1
Ka Yan
- 27
- 0
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!
Last edited: