- Determine whether the given sets are open, closed, neither open nor

closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...

2. the intersection of all the open intervals (0,(n+1)/n)

My guess:

1. open only

2. open only - Hello , me too i guess that the two sets are open

"If you judge people, you have no time to love them"

Mother Teresa

--- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a écrit :

De: Michelle Wynne <michwynne@...>

Objet: [MATH for FUN] Open or Close, neither, or both?

À: mathforfun@yahoogroups.com

Date: Lundi 1 Septembre 2008, 9h11

Determine whether the given sets are open, closed, neither open nor

closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...

2. the intersection of all the open intervals (0,(n+1)/n)

My guess:

1. open only

2. open only

------------------------------------

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[Non-text portions of this message have been removed] - [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed set is not always closed and this union tends to ]-1,1[ so it's an opened set

the enumerable intersection of an open set is an open set so the second one is open

"If you judge people, you have no time to love them"

Mother Teresa

--- En date de : Lun 1.9.08, Michelle Wynne <michwynne@...> a écrit :

De: Michelle Wynne <michwynne@...>

Objet: [MATH for FUN] Open or Close, neither, or both?

À: mathforfun@yahoogroups.com

Date: Lundi 1 Septembre 2008, 9h11

Determine whether the given sets are open, closed, neither open nor

closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...

2. the intersection of all the open intervals (0,(n+1)/n)

My guess:

1. open only

2. open only

------------------------------------

Yahoo! Groups Links

_____________________________________________________________________________

Envoyez avec Yahoo! Mail. Une boite mail plus intelligente http://mail.yahoo.fr

[Non-text portions of this message have been removed] - See the first exercises of chapter 2 in bartle: elements of Lebesgue integration for clues.

Michelle Wynne <michwynne@...> escreveu: Determine whether the given sets are open, closed, neither open nor

closed, or both open and closed.

1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...

2. the intersection of all the open intervals (0,(n+1)/n)

My guess:

1. open only

2. open only

---------------------------------

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[Non-text portions of this message have been removed] - --- In mathforfun@yahoogroups.com, Ahlem <is.dreams@...> wrote:
>

set is not always closed and this union tends to ]-1,1[ so it's an

> [-1+1/n,1-1/n] is a closed set but the enumerable union of a closed

opened set> the enumerableÂ intersection of an open set is an open set so the

second one is open

I think the intersection of a *finite* number of open sets is always

open, but this (infinite) intersection is the half open interval

(0,1] neither open nor closed.

>

Ã©critÂ :

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> "If you judge people, you have no time to love them"

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> Mother Teresa

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> --- En date deÂ : Lun 1.9.08, Michelle Wynne <michwynne@...> a

> De: Michelle Wynne <michwynne@...>

______________________________________________________________________

> Objet: [MATH for FUN] Open or Close, neither, or both?

> Ã: mathforfun@yahoogroups.com

> Date: Lundi 1 Septembre 2008, 9h11

>

> Determine whether the given sets are open, closed, neither open nor

> closed, or both open and closed.

>

> 1. the union of all the closed intervals [-1+1/n, 1-1/n], n=2,3,...

> 2. the intersection of all the open intervals (0,(n+1)/n)

>

> My guess:

> 1. open only

> 2. open only

>

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> Yahoo! Groups Links

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_______> Envoyez avec Yahoo! Mail. Une boite mail plus intelligente

http://mail.yahoo.fr

>

> [Non-text portions of this message have been removed]

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