Functions

• injective (one-to-one) - $f(x_1)=f(x_2)⟹x_1=x_2$. (Equivalently, $x_1\ne x_2⟹f(x_1)\ne f(x_2)$)
• surjection (onto) - $\forall y\in Y,\exists x\in X,f(x)=y$
• bijective (one-to-one correspondence, or invertible function ^[פונקציה הפיכה]) - injective+surjection

Theroems

• Theroem (3.25) - $f:A\to B$ is bijection $⟹f^{-1}:B\to A$ is bijection $\wedge$ $(f^{-1}{)}^{-1}=f$
• Theroem (3.26) - $f:A\to B$ is bijection $⟹f^{-1}\circ f=I_A\wedge f\circ f^{-1}=I_B$
• Theroem (3.27) - $f:A\to B,g:B\to A$, s.t. $g\circ f=I_A\wedge f\circ g=I_B⟹g,f$ are bijections, and $f^{-1}=g$