this post was submitted on 10 Dec 2024
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Jesus says that for every number in an empty set it is true that 1=2?
That’s formally correct, any property can be attributed to elements of an empty set - for example, every unicorn currently living in my house is afraid of tea.
This is counterintuitive because for this to be true you’d expect me to have to prove the existence of my unicorns and then their phobias, but formally speaking I just need for counter-examples to be impossible.
Logically speaking the negation of “all my unicorns are afraid of tea” is “at least one unicorn is not afraid of tea”, which is not possible since I have no unicorns, therefore my sentence is formally correct. Even though people wouldn’t accept this because it is counterintuitive.
Did I get the joke?
You got it bro. Should do something about those unicorns though, a civilized unicorn would drink tea.
By that logic, wouldn't "every unicorn is my house enjoys tea" also be *true*, because the negated "at least one unicorn in my house dislikes tea" can't be proven?
Yes, that's also true. The empty set is the only set for which every element has property A and doesn't have property A simultaneously.
For example:
If the Eiffel Tower is on the Moon, then 1=2 and 1≠2.
Agreed, that's why it's also true that every unicorn currently living in his house enjoys tea.