Thank you so much, this is the video I needed! You explain it from the grass root level. Most of these lecturers on TH-cam just jump straight into the hard core math stuff, no explanations no Vaseline.
Thank you thank you!! From reading the textbook, watching your videos, I was one of the few not lost in class last night! Prepping for next class trying to understand Quantifiers and you did it again! Huge thanks!!!
Also, if you want to stack quantifiers, be very careful of order. For a good informal example from Discrete Mathematics with Applications by Susanna S Epp, if L(x, y) is a predicate meaning “x loves y”, then AxEy L(x, y) means “Everyone has someone they love” (more formally, “For all people x, there is a person y such that x loves y”), but EyAx L(x, y) means, to quote the book, “that there is one truly amazing individual who is loved by all people” (“There is a person y such that for all people x, x loves y”). This ambiguity also comes across in the more informal English wording “Everybody loves somebody.” This is only when mixing E and A types; when the quantifiers are the same types, order doesn’t matter (ExEy and EyEx are the same). In fact, I was recommended this video by this online textbook thing called ZyBooks which I’m learning from, and provides a nice analogy for how the stacked quantifiers work. Basically, when evaluating a proposition with quantifiers, you can think of it as like a game between two players, E and A. These two fill in the variables in the proposition in order of the quantifiers; when A fills one in, it’s trying to make the proposition false, while E is trying to make it true. For example, with a statement like AxEy (x+y=0), the first turn goes to A, who may fill in x with any number, and wishes to make a false proposition. However, no matter what number he fills it in with, E can then pick a y=-x, so x and y sum to 0. Thus E wins, and the proposition is true. However, with EyAx (x + y = 0), E goes first; no matter what they fill in y with, A is free to choose any value other than -y for x, which makes the proposition false; thus A wins and it is false. For a slightly more complex example, try ExAy (abs(y + 1/y) > x). E goes first, and can fill in x. It turns out that if they pick any number less than 2, A is foiled; no matter what they put into y, y + 1/y never has an absolute value less than 2. As such, A loses and the proposition is true.
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.
Excellent teaching method, very clear, a little repetition and emphasis on key points, man this was very, very helpful. I will like, subscribe, and be back.
This is a good video, but it bears mentioning that the universal is usually translated as conditional, while the existential is a conjunction. Using your example, “Every dog is a mammal” can be more precisely translated as ∀x(Dx->Mx), where D is the predicate “is a dog”, and M the predicate “is a mammal”. It’s easy to see how an existential of the form “some A are B” is just a negated universal since a logically equivalent way of expressing the above example is ~∃x(Dx∧~Mx). An analogous case could be if the unique existential were introduced as a primitive quantifier without first showing that it can be expressed as ∃x∀y(Fx∧(Fy->y=x)).
My professor told me to buy a book and then write summaries based on it's horrific wording. Thank you for your work. I hope you're monetized and I hope this is a nice trickle of residual meals for the rest of your life.
These videos are epic! its almost perfect.... if only there was examples of how thee concepts could be applied on questions you would see in HW or tests this would be beyond amazing!
This is mostly teaching the shorthand, instead of teaching the matter itself. The matter itself is present but in focus is the Abbreviations it feels a bit backwards.
It looks like functional programming but the math has complicated notation. In javascript, we have .every() and .indcludes() functions witch is like "For all" and "There Exists"
@Trefor Bazett But how it can be both,I am precisely asking what does the definition of even numbers refers to.Or for simply,the definitions of chairs,tables,spoons etc refers to a class satisfying the stated property or these terms symbolise any object satisfying stated property. 2 is even number.True But in what sense?
Not all heroes wear cape.... but dude you deserve one..Thanks!!
Bro my teacher don't tell meaning of those symbol 😭
I’m literally watching rn in my math class.
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
This playlist might be the only thing keeping me sane for my Discrete class. THANK YOU SOOOO MUCHHHHHHH
your lectures helped me to get through my semister
I am grateful for the clarity of your breakdown of the problem. Thank you
You should be my lecturer. You are amazing. Thank you for the video.
Your tutorials are really educative. I have been educated so much by your tutorials thanks a lot. Now i have a real passion for mathematics 👍
Thank you so much, this is the video I needed! You explain it from the grass root level. Most of these lecturers on TH-cam just jump straight into the hard core math stuff, no explanations no Vaseline.
Your explantions and examples about the universal and existential quantifiers are so well.Thanks.
Thank you for making these videos. Your explanation is a lot easier to understand!
Thanks a lot for making this video, I really see your passion of demonstrating these concepts.
Hello I need help how can I find a Spanish teacher
this is more clearer than my previous math class
Thank you thank you!! From reading the textbook, watching your videos, I was one of the few not lost in class last night! Prepping for next class trying to understand Quantifiers and you did it again! Huge thanks!!!
Nice! Glad it helped:)
And then I wonder why are we paying the hefty tuition fees when it should be profs like Trefor who deserve it.
It is pathetic!My uni uses 100% TH-cam 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
Also, if you want to stack quantifiers, be very careful of order. For a good informal example from Discrete Mathematics with Applications by Susanna S Epp, if L(x, y) is a predicate meaning “x loves y”, then AxEy L(x, y) means “Everyone has someone they love” (more formally, “For all people x, there is a person y such that x loves y”), but EyAx L(x, y) means, to quote the book, “that there is one truly amazing individual who is loved by all people” (“There is a person y such that for all people x, x loves y”). This ambiguity also comes across in the more informal English wording “Everybody loves somebody.” This is only when mixing E and A types; when the quantifiers are the same types, order doesn’t matter (ExEy and EyEx are the same).
In fact, I was recommended this video by this online textbook thing called ZyBooks which I’m learning from, and provides a nice analogy for how the stacked quantifiers work. Basically, when evaluating a proposition with quantifiers, you can think of it as like a game between two players, E and A. These two fill in the variables in the proposition in order of the quantifiers; when A fills one in, it’s trying to make the proposition false, while E is trying to make it true.
For example, with a statement like AxEy (x+y=0), the first turn goes to A, who may fill in x with any number, and wishes to make a false proposition. However, no matter what number he fills it in with, E can then pick a y=-x, so x and y sum to 0. Thus E wins, and the proposition is true. However, with EyAx (x + y = 0), E goes first; no matter what they fill in y with, A is free to choose any value other than -y for x, which makes the proposition false; thus A wins and it is false.
For a slightly more complex example, try ExAy (abs(y + 1/y) > x). E goes first, and can fill in x. It turns out that if they pick any number less than 2, A is foiled; no matter what they put into y, y + 1/y never has an absolute value less than 2. As such, A loses and the proposition is true.
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.
Ah thank you very much for this clarification. I was getting confused at the exact same thing and the book I am using doesn't state this.
Thanks Sir, Made me Understands more than my lecturer.
Your explanation in easy to understand than my teacher
Glad it helped!
Very nice explanation sir,
I love watching your videos
You explain it clearly and very nicely
🥰🥰🥰🥰🥰
Love from INDIA
Very helpful video...and great use of technology👍👍
Thanks so much for this most helpful video. I've been studying maths for 16 months now. I love it. It's something I cannot not do.
I love how these videos end, it's a literal mic drop. 🎤
I'm so grateful for these videos. Thank you
Didn't find a better explanation. Thank you.
I can't understand my professor because of his accent. Thank you so much
I hope I don’t have a teacher that I can’t understand
feel you fam
🤣
@@vishnu.s_ hes talking bout u
Your videos are just mind-blowing ..it helped me a lot thankyou so much ☺️☺️
My pleasure 😊
you are the best
Im gonna take u as my maths teacher.
Thank you!
Thank you so much for this. i was really struggling with understanding it but you made it so simple.
Well prepared, thanks for the explanation
Thx so much better than my teacher
You're welcome 😊
All dogs are mammals and at least one of them is called spot.
your lessons are short but good
Çoox gözəl izah verdiniz!, təşəkkür edirəm! 🍀👍
Excellent teaching method, very clear, a little repetition and emphasis on key points, man this was very, very helpful. I will like, subscribe, and be back.
😲Do you write inverted on glass?or editing.superb pretty understandable👌
Best channel☺😀😊
thanks a lot . love from india . well explained 👍👌
Thank you Dr Trefor ☺
Wow
I need this man to be my teacher ✌️
He explained everything cleanly
It confuse me more how he can write like that than the lecture itself
I love ur video sir, just wish I can tap into ur blessings
literally the best
Thank you sir, clear this topic.
Amazing explanation about this term. Thank you Trefor!
you are simply great
My prof is too lazy to teach us online so she gave us module but we can't understand a thing, Thank you for this!
That's so frustrating!
@@DrTrefor That's what they called the new normal. My classmates keeps asking how to do it but none of us know because we can't understand the module.
thanks doc ur lectuers helped me ............. from Egypt
This is a good video, but it bears mentioning that the universal is usually translated as conditional, while the existential is a conjunction. Using your example, “Every dog is a mammal” can be more precisely translated as ∀x(Dx->Mx), where D is the predicate “is a dog”, and M the predicate “is a mammal”. It’s easy to see how an existential of the form “some A are B” is just a negated universal since a logically equivalent way of expressing the above example is ~∃x(Dx∧~Mx).
An analogous case could be if the unique existential were introduced as a primitive quantifier without first showing that it can be expressed as ∃x∀y(Fx∧(Fy->y=x)).
Thank you!
Excellent Lecture
Really appreciate your explanations. Helps me a lot!
Great explanation, very clear voice.
Thank you
My professor told me to buy a book and then write summaries based on it's horrific wording. Thank you for your work. I hope you're monetized and I hope this is a nice trickle of residual meals for the rest of your life.
You've helped me alot sir thank you
great great , understandable to the core and helpful !!
Thanks Brother.... It helps me a lot... Again thanks
Very clear explanation and cool display, thank you so much!
Does he write mirrored? Damn thats cool
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
thank you, very helpful!
Thank you so much! This was really helpful.
No matter how good the teacher is i will never feel the meaning t
Of these wierd @$ confising symbol 😭😭😭
Clearly explained. Thank you.
These videos are epic! its almost perfect.... if only there was examples of how thee concepts could be applied on questions you would see in HW or tests this would be beyond amazing!
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
9:30 min video > 1 week lecture 👍👍
so much better than my professors lol thanks!
haha, glad it helped!
@@DrTrefor so such that can be written as, too
Very useful content! Glitch in the matrix at 2:08
Very cool Board and Discussion
Awesome
Thanks Sir
With rescept from The University of Lahore
This is mostly teaching the shorthand, instead of teaching the matter itself. The matter itself is present but in focus is the Abbreviations it feels a bit backwards.
He is so motivated 😍
The fact that I have been pronouncing predict the wrong way bruhh
it was already going great but went gangsta real quick when he started writing on the glass like a boss.
Thanks , sir this video is beneficial for us
really great
Thank you teacher.
good job
Excellent video thanks.
YOU ARE AMAZING!!
"My exes are gonna be animals" Truer words have never been spoken
i love you
You should have something that denotes in which order the videos should be seen. Like Chapter 1, Chapter 2 or 1.1, 1.2, etc.
Wonderful explained sir 🤘
you are great. I want say, thank you for lecture!!!
It looks like functional programming but the math has complicated notation. In javascript, we have .every() and .indcludes() functions witch is like "For all" and "There Exists"
thank you so much for the help!! hopefully i wont fail this class now
One of the best videos I was struggling to find out ! (Y)
@Trefor Bazett But how it can be both,I am precisely asking what does the definition of even numbers refers to.Or for simply,the
definitions of chairs,tables,spoons
etc refers to a class satisfying the stated property or these terms symbolise any object satisfying stated property.
2 is even number.True
But in what sense?
Great!
Insted of: For all x in D , P(x)
Just write: (x in D) => (x in P(x))
Edit: Try to replace exsist
9:30 min video > 1 week lecture 👍
super useful, thannk you
Awesome explaination. Thanks alot sir.
Wow I like it. Keep it up.
Thank you very much very helpful
Bro, I was just looking for some Turn ∀ Gundam videos. How did I end up here?
Thank you sir
Do you have a video of choice function and scope?
It's like Plato's forms and essences but put into a symbolic notation? Well, this is cool
thank you sir. I've deep understand the lesson I'm reading on my book.