Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists" 

TheBrownBear when some random video on youtube makes you understand more than when your teacher teaches you

i was today too 🙃

I'm literally shaking and crying right now

Proud of you

Cheers ​@@walltuhwhite

Bro my teacher don't tell meaning of those symbol 😭

Hello I need help how can I find a Spanish teacher

Nice! Glad it helped:)

Too long

Thanks a looot buddy

The analogy of E (the existential quantifier, symbolized by ∃) and A (the universal quantifier, symbolized by ∀) as players in a game is a conceptual way to understand how quantifiers work in predicate logic. Here's how the two "players" are defined in this context: E (Existential Quantifier ∃): When ∃ precedes a variable, it means "there exists" or "there is at least one." The goal of the E player in this analogy is to find at least one instance that makes the statement true. E is satisfied with finding a single example that works. A (Universal Quantifier ∀): When ∀ precedes a variable, it means "for all" or "every." The goal of the A player is to ensure that the statement is true for every possible instance. A wants the statement to hold universally, without exception. When these quantifiers are "stacked," or placed in sequence, it creates a game-like scenario where E and A take turns "choosing" values for the variables they are quantifying, with their goals opposed. E tries to prove the statement true, while A tries to prove it false. The order of the quantifiers is crucial because it determines the order of play in this game. Let's use your examples to explain the analogy: AxEy (x + y = 0): A's turn (Universal Quantifier ∀x): A must pick a value for x that it believes could lead to the proposition being false for some y. E's turn (Existential Quantifier ∃y): After A picks x, E tries to find a value for y that makes x + y = 0 true. Outcome: E can always pick y = -x to make the equation true, regardless of A's choice. Therefore, E wins, and the proposition is true for all x. EyAx (x + y = 0): E's turn (Existential Quantifier ∃y): E must choose a value for y hoping to make the proposition true for all x. A's turn (Universal Quantifier ∀x): A will then try to find a value for x that does not satisfy the equation x + y = 0, aiming to prove the proposition false. Outcome: No matter what E chooses for y, A can always choose an x that is not equal to -y, making the proposition false. Therefore, A wins, and the proposition is false because it does not hold for all x. ExAy (abs(y + 1/y) > x): E's turn (Existential Quantifier ∃x): E needs to pick an x such that no matter what y is chosen afterward, the inequality abs(y + 1/y) > x will be true. A's turn (Universal Quantifier ∀y): A will then try to pick a value for y to disprove the inequality for the chosen x. Outcome: If E chooses any x less than 2, A cannot find a y to make the inequality false, because the absolute value of y + 1/y is always at least 2 (achieved when y=1 or y=-1). Therefore, E wins, and the proposition is true. The takeaway from this analogy is that the order in which you stack quantifiers fundamentally changes the meaning of a logical expression, and understanding this interaction can help determine the truth value of complex statements in predicate logic.

It is pathetic!My uni uses 100% RU-vid content. I'm basically paying lots of money for 100% self-study .

In the end we pay for a piece of paper that proves our competence, not the competence itself

Oh same. I am learning this at my own pace because it was too hard to learn it at my uni's pace. This is 100 times better and more fun to learn than whatever we had at uni.

I’ve long thought of building out an official course, but it’s still a long time away

@@DrTrefor do you offer tutoring haha ill pay per hour lol

My pleasure 😊

I hope I don’t have a teacher that I can’t understand

feel you fam

🤣

@@vishnu.s_ hes talking bout u

@@DrTrefor ohhhhh that makes sense to envision it that way LOL thanks so much, i'll let my classmates know in our discussion board that you're not writing backwards hahah :D

Trefor Bazett Thank you very much😊

Trefor Bazett ok I’ll go through it. Thanks

@@DrTrefor Yes, I can catch that. I found few books or academic modules use that kind of writing style, but honestly it's bothering when I read it. Your explanation in the video is awesome. Thanks a lot, sir!

Thank you!

Glad it helped!

You're welcome 😊

Smart board does the same thing bro

Lol came to comments section for this question

no . He writes and then they flip the video

haha i wish i spent years mastering writing mirrored, but sadly just flipped it on the computer:D

Lmao

haha, glad it helped!

@@DrTrefor so such that can be written as, too

@@DrTrefor Thank you sir! I appreciate it a lot, my favorite Math Professor 🙆‍♀️