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I'm not sure about this expression:\[\emptyset \subset \{\emptyset\}\], I think it's false.
 one year ago
 one year ago
I'm not sure about this expression:\[\emptyset \subset \{\emptyset\}\], I think it's false.
 one year ago
 one year ago

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NodataBest ResponseYou've already chosen the best response.0
This is read: The empty set is a proper subset of the set containing only the empty set.
 one year ago

joemath314159Best ResponseYou've already chosen the best response.1
The empty set is a subset of any set, regardless of whats in it.
 one year ago

RitiBahl100Best ResponseYou've already chosen the best response.0
A is a subset of B if and only if for all elements x of A, x is in B. This is vacuously true, since there are no elements x of the empty set. Hence, the empty set is a subset of the empty set
 one year ago

NodataBest ResponseYou've already chosen the best response.0
Yeah, I know it's true for the subsets, but I mean the PROPER subset
 one year ago

joemath314159Best ResponseYou've already chosen the best response.1
Proper just means the sets arent equal. So the fact that the empty set is a subset of every set, even though every set isnt empty, means its a proper subset of any non empty set.
 one year ago

NodataBest ResponseYou've already chosen the best response.0
Ohh than you @joemath314159 now I got it clear.
 one year ago
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