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March 9th, 2014, 04:51 PM   #1
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Is this statement true?

my first post !

im wondering, can we correctly say :
a set cotaining the Empty Set is equal to the Empty Set
ie does The Empty set = {The Empty Set}

or is this like saying "...the number 5 is equal to {5}..." which it obviously is not...

thanx
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March 9th, 2014, 06:00 PM   #2
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Re: Is this statement true?

Quote:
Originally Posted by danielphillis
my first post !

im wondering, can we correctly say :
a set cotaining the Empty Set is equal to the Empty Set
ie does The Empty set = {The Empty Set}

or is this like saying "...the number 5 is equal to {5}..." which it obviously is not...

thanx
Grocery bags. I have an empty grocery bag. It's an empty bag. Now I put inside of it another empty bag. Now my original bag is no longer empty: it contains an empty bag.

If you ever asked a grocery clerk to "Double bag it, please," then you saw them put an empty bag inside of a bag. The outer bag is not empty; it contains a bag. The inner bag is empty.
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March 9th, 2014, 06:06 PM   #3
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Re: Is this statement true?

Quote:
Originally Posted by Maschke
Grocery bags. I have an empty grocery bag. It's an empty bag. Now I put inside of it another empty bag. Now my original bag is no longer empty: it contains an empty bag.

If you ever asked a grocery clerk to "Double bag it, please," then you saw them put an empty bag inside of a bag. The outer bag is not empty; it contains a bag. The inner bag is empty.
Good explanation! I may steal it.

To be clear: the empty set { } is different from the set containing only the empty set, { { } }.
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