Build a bijection between $mathcal{P}(mathbb{Z}^+)$ and $mathcal{P} (mathbb{Z})$
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I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?
functions
asked Nov 15 at 5:13
Umuko
945
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I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?
functions
asked Nov 15 at 5:13
Umuko
945
2
I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17
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up vote
0
down vote
favorite
up vote
0
down vote
favorite
I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?
functions
asked Nov 15 at 5:13
Umuko
945
I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?
functions
functions
asked Nov 15 at 5:13
Umuko
945
asked Nov 15 at 5:13
Umuko
945
asked Nov 15 at 5:13
Umuko
945
asked Nov 15 at 5:13
Umuko
945
asked Nov 15 at 5:13
Umuko
945
945
2
I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17
add a comment |
2
I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17
2
2
I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17
I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17
add a comment |
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2
I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17