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## Main Question or Discussion Point

I am struggling with combining infinite unions with infinite intersections, the problem i have is to show that, for Sets A

∞....∞

[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] A

i=0 j=0

is equal to

.....∞

[itex]\bigcap[/itex]{([itex]\bigcup[/itex]A

..... i=0

please could someone point me in the right direction,

I can show that

∞....∞

[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] A

i=0 j=0

is a subset of

∞....∞

[itex]\bigcap[/itex] ( [itex]\bigcup[/itex] A

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!

_{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!