I am struggling with combining infinite unions with infinite intersections, the problem i have is to show that, for Sets A(adsbygoogle = window.adsbygoogle || []).push({}); _{ij}where i,j [itex]\in[/itex]N (N=Natural Numbers)

∞....∞

[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] A_{ij})

i=0 j=0

is equal to

.....∞

[itex]\bigcap[/itex]{([itex]\bigcup[/itex]A_{ih(i)}:h[itex]\in[/itex]N^{N}}

..... i=0

please could someone point me in the right direction,

I can show that

∞....∞

[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] A_{ij})

i=0 j=0

is a subset of

∞....∞

[itex]\bigcap[/itex] ( [itex]\bigcup[/itex] A_{ij})

i=0 j=0

however i am struggling with the function h(i) used in the above question to make the two sets equal

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Infinitary union combined with infinitary intersection

Loading...

Similar Threads for Infinitary union combined |
---|

B Combinations of n elements in pairs |

I Combinatorics & probability density |

I A specific combination problem |

I Combination of Non Adjacent Numbers |

B Arranging blocks so that they fit together |

**Physics Forums | Science Articles, Homework Help, Discussion**