- #1
bert2612
- 5
- 0
I am struggling with combining infinite unions with infinite intersections, the problem i have is to show that, for Sets Aij where i,j [itex]\in[/itex]N (N=Natural Numbers)
∞...∞
[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] Aij)
i=0 j=0
is equal to
...∞
[itex]\bigcap[/itex]{([itex]\bigcup[/itex]Aih(i):h[itex]\in[/itex]NN}
... i=0
please could someone point me in the right direction,
I can show that
∞...∞
[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] Aij)
i=0 j=0
is a subset of
∞...∞
[itex]\bigcap[/itex] ( [itex]\bigcup[/itex] Aij)
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!
∞...∞
[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] Aij)
i=0 j=0
is equal to
...∞
[itex]\bigcap[/itex]{([itex]\bigcup[/itex]Aih(i):h[itex]\in[/itex]NN}
... i=0
please could someone point me in the right direction,
I can show that
∞...∞
[itex]\bigcup[/itex] ( [itex]\bigcap[/itex] Aij)
i=0 j=0
is a subset of
∞...∞
[itex]\bigcap[/itex] ( [itex]\bigcup[/itex] Aij)
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!