For the existential quantifier ∃ can I take it as meaning
"there exists at least one"
or does it mean
"there is only one"
"there exists at least one"
or does it mean
"there is only one"
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It means ... "exist at least one"... for example in the set { 2,3,4,5,6,7,8,9}
we can say in the set ∃ x so that x is an odd number. There are more then one.
we can say in the set ∃ x so that x is an odd number. There are more then one.
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There exists at least one.
Where Shakespeare wrote "There is something rotten in the state of Denmark."
The mathematician would say.
∃ x, member of the set Denmark, that has the property of rottenness.
If I could figure out how to get all the mathematical objects into the text, I could make it even more dull..
The upside down A means "for all"
As in.....
it is not the case that for all x, members of Denmark, all are not rotten.
Where Shakespeare wrote "There is something rotten in the state of Denmark."
The mathematician would say.
∃ x, member of the set Denmark, that has the property of rottenness.
If I could figure out how to get all the mathematical objects into the text, I could make it even more dull..
The upside down A means "for all"
As in.....
it is not the case that for all x, members of Denmark, all are not rotten.
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there exists an integer with a certain property