ChinaNumber1Fan
Greycel
★
- Joined
- Jun 3, 2019
- Posts
- 34
Ok, so for some bizarre reason, people don't seem to understand the difference between ∀∃ and ∃∀ (for those of you not familiar with the notation, '∀' means 'forall', and '∃' means 'there exists'). Now if I ever have to tutor a young boy this, I already have just the right intuition. For one we want to think about these quantifiers as 'relations'. This sounds less vaguer in my head so let me elaborate.
Let's have a set A of objects {a_1,a_2, ...} and set B of objects {b_1,b_2, ...}. Now we also have a set of objects and their relations, R = {(a_i, b_j), a_i and b_j are related}. Now let's look at the differences with these 2 structures.
With ∀x∈A∃y∈B|(x,y) we have the rule that each object has at least 1 partner. This means that there doesn't exist an a_i in S that there is no (a_i, b_j) in R. Now, this is a somewhat ideal world. We haven't ruled out the polygamous condition, but in the very least everyone has somebody. (If we wanted monogamy, we'd use '∃!'.
However, let's look at ∃x∈S∀y∈S|(x,y). This shit. This shit right here is what I'd like to call the blackest of all pills. This one dude is fucking every single female. Just think about this for a moment. Imagine some emperor of man tier giga-chad that is 60ft tall and has a 15 foot monster cock roaming around the planet impregnating every woman he sees. This is the type of stuff we'd be dealing with.
So gentlemen, I hope you do not mix your quantifiers again.
Let's have a set A of objects {a_1,a_2, ...} and set B of objects {b_1,b_2, ...}. Now we also have a set of objects and their relations, R = {(a_i, b_j), a_i and b_j are related}. Now let's look at the differences with these 2 structures.
With ∀x∈A∃y∈B|(x,y) we have the rule that each object has at least 1 partner. This means that there doesn't exist an a_i in S that there is no (a_i, b_j) in R. Now, this is a somewhat ideal world. We haven't ruled out the polygamous condition, but in the very least everyone has somebody. (If we wanted monogamy, we'd use '∃!'.
However, let's look at ∃x∈S∀y∈S|(x,y). This shit. This shit right here is what I'd like to call the blackest of all pills. This one dude is fucking every single female. Just think about this for a moment. Imagine some emperor of man tier giga-chad that is 60ft tall and has a 15 foot monster cock roaming around the planet impregnating every woman he sees. This is the type of stuff we'd be dealing with.
So gentlemen, I hope you do not mix your quantifiers again.