Hi, I am having problems with proving the double containment argument for the following problems. I would appreciate any feedback. Thanks.(adsbygoogle = window.adsbygoogle || []).push({});

Compute [tex]\bigcup[/tex] (i [tex]\in[/tex] I) Ui and [tex]\bigcap[/tex] (i [tex]\in[/tex] I) Ui if

a. I=N, the set of all positive natural numbers and U_n = (-n,n) [tex]\subseteq[/tex]R(U_n is the open interval between -n and n)

i.

[tex]\bigcap[/tex] (i [tex]\in[/tex] I) Ui = (infinity)

How do I prove the double containment argument?

Do I say that if x is not equal to infinity then there exists a number such that x=1?

ii.

[tex]\bigcup[/tex] (i [tex]\in[/tex] I) Ui = (-1,1)

Do I write is x is a member of (-1,1) then there exists a number such that |x| < 1 or 1< 1/|x|

b. I=N, the set of all real numbers and U_r = (0, 1/(1+r^2)) [tex]\subseteq[/tex]R(U_r is the open interval between 0 and 1/(1+r^2))

i.

[tex]\bigcap[/tex] (i [tex]\in[/tex] I) Ui = (0,0)

For the double containment argument do I write what if x is not equal to 0?

ii.

[tex]\bigcup[/tex] (i [tex]\in[/tex] I) Ui = (0, 0.5)

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Infinite Operations with Sets

Loading...

Similar Threads for Infinite Operations Sets |
---|

A About the “Axiom of Dependent Choice” |

I Problem with infinite decimal numbers? |

I Can you calculate probability with infinite sets? |

I Cardinality of the Power Series of an Infinite Set |

I Logical Operators Assistance |

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