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Math Help - Set Theory

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    Set Theory

    Suppose the the set N of natural numbers is less than or equimunerous to A. Show that A is infinite. Infinite is defined as not having a bijection.
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    Quote Originally Posted by taypez View Post
    Suppose the the set N of natural numbers is less than or equimunerous to A. Show that A is infinite. Infinite is defined as not having a bijection.
    By definition if |N|<|A| the there is a injection from N to A.
    Now, if there were a bijection from A to a finite subset of N then that leads to a contradiction. Therefore A must be infinite.
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