Question

Prosze o pomoc
Zbiór zadań matematyka rozszerzona 1 zadanie 1.25/11

Answer 1

Pamiętamy:

• ZERO nie jest liczbą ani dodatnią ani ujemną

Dla przypomnienia:

[tex]\mathbb{Z} =\{...,-3,-2,-1,0,1,2,3,...\}\\\\ \mathbb{Z_{+} }=\{1,2,3,...\}\\\\ \mathbb{Z_{-} }=\{...,-3,-2,-1\}\\\\\mathbb{N }=\{0,1,2,3,...\}\\\\\mathbb{N_{+} }=\{1,2,3,...\}[/tex]

[tex]\huge\boxed{zad.1.25}\\\\\boxed{a}~~A=\{x:x=\dfrac{1}{n} ~\land~n\in \mathbb{N_{+} } \}~~\Rightarrow~~A=\{1,\dfrac{1}{2} ,\dfrac{1}{3} ,\dfrac{1}{4} ,\dfrac{1}{5} ,...\}\\\\\boxed{b}~~A=\{x:x=2^{n} ~\land~n\in \mathbb{N_{+} } \}~~\Rightarrow~~A=\{2^{1} ,2^{2} ,2^{3} ,2^{4} ,2^{5} ,...\}=\{2,4,8,16,32,...\}[/tex]

[tex]\huge\boxed{c}~~A=\{x:x=4k ~\land~k\in \mathbb{Z} \}~~\Rightarrow~~A=\{...,-12,-8,-4,0,4,8,12 ,...\}\\\\\boxed{d}~~A=\{x:x=3k ~\land~k\in \mathbb{Z_{-} } \}~~\Rightarrow~~A=\{...,-12,-9,-6,-3\}[/tex]

[tex]\huge\boxed{e}~~A=\{x:x=n^{2} ~\land~n\in \mathbb{N } \}~~\Rightarrow~~A=\{0^{2} ,1^{2} ,2^{2} ,3^{2} ,4^{2} ,...\}=\{0,1,4,9,16,...\}\\\\\boxed{f}~~A=\{x:x=k^{3} ~\land~n\in \mathbb{Z_{+} } \}~~\Rightarrow~~A=\{1^{3} ,2^{3} ,3^{3} ,4^{3} ,...\}=\{1,8,27,64,...\}[/tex]