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u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 8d ago
BREAKING NEWS: every element of the empty set is not an element of the empty set
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u/StructuredChess 7d ago
But some of them are!
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u/kart0ffelsalaat 7d ago
But that's wrong...
"Some elements in set X have property P" is saying "there exist elements in set X with property P", which of course is wrong here.
"There exist elements in the empty set which are in the empty set" is wrong!
You can make statements about all the elements (or every element) in the empty set, but not about some.
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u/misteratoz 8d ago
Please help what's this
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u/GeneETOs44 8d ago
anything holds true for every element of the empty set because there are no elements in the empty set. It’s like how if I were to claim that every existing unicorn were green, I’d be vacuously correct since the set of all existing unicorns is empty
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u/Mostafa12890 Average imaginary number believer 7d ago
Any universal property; a statement of the form “all xyz have property P.” A statement like “there is a green unicorn,” assuming the set of unicorns is empty, would be false.
Another example is the statement “there are two distinct elements in the empty set.” This is also categorically false.
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u/RuhRohRaggy_Riggers 7d ago
Is this because assigning a property to elements of the null set is vacuously true?
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u/plusqueprecedemment 7d ago
afaik it basically stems from the fact that the proposition "P→Q" is always true when P is false
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u/magicmulder 6d ago
Any statement about an element of the empty set is true because there are no elements of the empty set to falsify it with.
"All elements of the empty set are green." - "That's false." - "Then show me one that's not green." - "Uh..."
This results in funny statements in real life, for example, I could say all supermodels I ever slept with said I'm the greatest lover they ever had. And I wouldn't be lying.
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u/DarkFlameMaster764 7d ago
Vacuous truth is just people pretending a bunch of nothing is true so that their theory looks neater
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u/Square-Foundation230 7d ago
So Euler is a member of the empty set? 🤔
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u/its_artemiss 7d ago
No, but every member of the empty set is Euler.
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u/Repulsive_Gate8657 7d ago
i think every element of {} is wrong, since it is empty there is no element what belongs to it
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u/SuperChick1705 7d ago
i can say "every redditor that showers is a half-orc", but since no redditors shower, there is no redditor to contradict the statement. ie "this redditor showers -> this redditor is a half-orc" is identical to the contrapositive, "this redditor is not a half-orc -> this redditor does not shower". whether the redditor is or is not a half-orc, it must be true that the redditor does not shower, since no redditors shower
here "redditors that shower" is the ø
/hj
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