Negating Logical Statements with Multiple Quantifiers

[@karenl4144]

Why KZbin tutorials always better than school teachers ?

[@lol-nd5it]

@@amantiwari814 it is.... you study this at university level proof. im doing it right now in my proof and analysis class

[@zerouno4477]

Simplest answer they have script

[@jadendodoo4979]

for real

[@IyadREZAZGUI]

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[@matthewrister]

Congratulations on mastering the ability of taking complex subjects and breaking them down into simple concepts that are easy to understand. The world needs more teachers like you. Thankfully, KZbin exists which allows for all users worldwide to benefit from your superb teaching style.

[@IyadREZAZGUI]

watch uthman ibn farooq

[@MULTIFACEPLANTER]

Wow... can't tell you how much your discrete mathematics videos have helped me

[@DrTrefor]

So glad they’re helping!

[@mountaindew68]

I am honestly kind of a moron and it's been a decade since I last studied college-level math. I went back to school this year and I might be too dumb to grasp discrete math, but these videos give me hope.

[@nipunkavishka]

Best tutorial ever.....

[@muslim_2000s]

offff , finally I found someone who thinks as I do ❤❤❤❤

[@kupinaa]

The video is great! I love it!! But there seems to be a loophole in the "Some number in D is the largest" statement. If we look at the "math translated" version of the statement, there exists a domain D, such that these two statements would not be equivalent. eg. D = {1, 1, 1, 1}. The math version would be true, because there exists 1 which is greater or equal then every other element of set D. But the english version would not be, because there isn't a number in the set which is the largest. As I understood it, the property should have contained a negation of x = y, and should have looked something like this: There exists some x in D, such that for all y in D, y ≠ x and x > y. I also want to thank you for such a great Discrete math course! It's absolutely awesome!

[@tod9141]

Right, but y ≠ x is redundant when there is a "" sign by definition, but I get what you're saying! I think Dr. Bazett should've written just "x > y" !

[@mohamedrashad8616]

Perfect! I was scared of those symbols before I watched this video but look at me now.

[@yash1152]

7:05 > _"for everything _*_else_*_ in the domain"_ small nitpick, i think the else part would require explicilty removing it from domain like D - {x}, in the current form in video, this just means all values in domain (x included); am i right?

[@Forkythechanter]

I wish more video like this exists but then universities will go out of business because more people can learn the materials on theirs own without ever have to spend money out of their pockets.

[@limonyomcgwa1664]

I appreciate this lesson

[@wangke6257]

Your explanation is so clear! I think if I were your student, you will be my most favourable teacher!

[@AbhishekBade1310]

his board is so trippy. like he is writing from behind it and we can everything the right side. and also he can see the text question in real time from his computer on his board. Damn

[@bababeebee123]

You're a legend man, thanks for the help!

[@hehexd8370]

you beast, saved me this day

[@alejandrodavidrodriguez7038]

Helped me understand this topic, thank you so much. I would say to go over some more complex examples and explain it in pure English. Other than that, great video!!!

[@anishjoshi1999]

love from nepal ..best lesson ever

[@ComtesseV]

You da best

[@manobray1800]

Sir you are really good teacher

[@natu.d9546]

You just saved my life

[@entoniworkout]

you saved my day G

[@yeab_sera1532]

Thank you so much for this video

[@VicksGamingWorld]

Great explanation

"Some number in D is the largest", can I use (imho simpler) version something like MAX(x) instead of P(x) ?

[@truthphilic7938]

sir, how do you sync animation with your movement?

[@Darttttk]

Regardless of how big my ex is, there is an even bigger 'why?'

[@amantiwari814]

Which books to use for discrete mathematics , I am bigginer

[@DrTrefor]

Here is a good free one: discrete.openmathbooks.org/dmoi3/

[@amantiwari814]

@@DrTrefor thank you

[@yash1152]

1:41 1:47 > _"still think of it as a property of x [P(x)]_ ... _because I've quantified my y"_ ahwww, awesome. yeah, i forgot that a variable/predicate quantified becomes like a constant/statement.

[@kutayalpdogdu2834]

Thank you bro

[@yash1152]

1:41 1:47 > _"still think of it as a property of x_ [P(x)] ... _because I've quantified my y ..."_ ahwww, awesome. yeah, i forgot this: a predicate quantified becomes a statement.

[@saisandeepchenna4796]

Sir u deserve 10m+ subscribers. I hope It will.

[@saisandeepchenna4796]

sorry sir ....... It is a typing error..... I mean 10m+ subscribers. I like the way you teach. Thank you very much sir.

[@AedAlore]

this lesson is gooooooood!1!!1!!

[@tothespace2122]

I have question: Why is the statement "Every integer has a larger integer" true but it's negation, although expected to be false, doesn't actually seem to be false to me? When prooving the statement ""Every integer has a larger integer", Trefor Bazett says you can take any integer x, add 1 to it and get an integer bigger than x. But when prooving the negation of the same statement, Trefor says "There is just no number out there that is bigger than everything else…", but that contradicts the reasoning used to prove the statement is true. I would be thankful if someone can clarify this a little bit to me.

[@duwartstewart5639]

Its negation is that there exists a number, that every other number is smaller than that number. Is false because integers can keep increasing. There is no number that is bigger than everything because there is always a bigger integer.

[@tothespace2122]

@@duwartstewart5639 I get it now. One has to be careful how he reads these statements. Thank you for the answer.

[@thomaslu3096]

Just out of curiosity, what is the difference between the following statements? ∀x∈D, ∃y∈D, L(y,x) → H(x) ∀x∈D, [∃y∈D, L(y,x)] → H(x)

[@thomaslu3096]

@@DrTrefor Thanks. I wasn't sure if the IF for the first one applied to the whole left side, or just L(y, x)

[@tagerauen5378]

Are you writing backwards, or did you reverse the video?

[@hamdimohammed2541]

You know what I like about logic? When you flip it and get an absolute nonsense. 4:33

[@ErikTheEbikeExpert]

Good luck at UVic!

[@xuepingsong5329]

im having so much trouble understanding multiple quantifiers in epsilon delta definition of limit

[@ppchavan001]

4:44 isn't infinity the largest integer? and if it is, the negated statement would be True as we!!

[@ppchavan001]

@@DrTrefor hmm...

[@BEN-hl6yt]

Infinity is not an integer, it is a limit.

[@gold4963]

No. Infinity is an idea, not an actual number. So, it can't be treated as such.

[@shoenicefan9229]

I LOVE YOU!!!!!

[@handyhacker11]

Kudos to you for writing backwards

[@handyhacker11]

nvm i bet it's just flipped around

[@Falkraath]

thanks

[@jhomwan6968]

Is he writing all the things backward?

[@ABSP5766]

No. The image is flipped. Look at the buttons of his shirt. They are in the "wrong" side for a man.

[@badaltripathi2648]

​@@DrTrefor If you compare the buttons of your shirt with that of the female's shirt, then you will understand what is he talking about. But thanks for making such an amazing course.

[@kriskanchi7469]

I wish there was a longer statement lolll my teacher put some super long ones on my test and it gets confusing

[@DrTrefor]

Honestly longer ones are challenging mostly because there are just symbols everywhere, but they are only doing exactly what we did in this video over and over again

[@EpicZombieGT]

Thank you niggation

[@EpicZombieGT]

Your welcome

[@joshkung]

How is he writing backwards thats impressive

[@VictorZamanian]

My god this voice. Excellent explanations but I feel like you are yelling this information at me.

[@manobray1800]

I like u sir

[@JesseBourretGheysen]

is he writing backwards?

[@hamedhosseini2155]

How do you write on the board? Are you writing backward? if yes you are my god man😂

[@sarkersaadahmed]

1:06 "bigger than my x"

[@SaraAit-qb8jq]

I hate Math, I really hate math !

[@Pspklove]

when you dont have a largest number then you also domt have a smallest numcer

[@Shridhar_Thorat]

Saviour. XD

[@yash1152]

1:41 1:47 > _"still think of it as a property of x [P(x)]_ ... _because I've quantified my y"_ ahwww, awesome. yeah, i forgot that a variable/predicate quantified becomes like a constant/statement.