Ivan Shishkin, Birch Grove

Bijective map

Definition / Mathematical formalism /

Also known as: Bijection

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A bijection, or bijective map, is a map that is both injective and surjective.

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  • Démontrer que les applications suivantes sont des bijections:
    1) f ⁣:{Z⟶Zn⟼n+2f \colon \left\{ \begin{array}{l} \Z \longrightarrow \Z \\n \longmapsto n+2 \end{array} \right.

    2) g ⁣:{R⟶Rx⟼2x+1g\colon \left\{ \begin{array}{l}\R \longrightarrow \R &\\ x \longmapsto 2x+1\end{array}\right.
    3) hh qui a toute partie de N\N associe son complémentaire.

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