I can't thank you enough for making these videos! The professor for my class believes the students can learn this stuff just by working in groups and without the professor lecturing at all and it's NOT working for me. I failed my first exam and was debating on dropping out but you give me hope this may not be the end XD Thank you!!
Thank you so much for clarifying this! I'm currently taking this class at my University and my professor talked about this topic in a 6min video, which I did not understand. Watching your video... I finally understand.
Thanks a ton Trefor! Your playlist has helped me immensely in understanding the subject, to the extent that I have started admiring the concepts involved in it. You teach extremely well and lucidly. 🙏
Hello professor! Do you think this would also conform to defining what an odd integer is(?): n is an odd integer if ∃k∈ℤ|n=2k+1∨-1 I hope I get an answer from you Thank you, Punkrider
What would happen if we defined an odd integer as "an integer n1 such that, for some integer k and another odd integer n2, n1 = 2k + n2?" In logic, is there a term to describe definitions like these in which the thing we are defining is in the definition itself? This could, instead, be a proof for "the sum of an even and odd integer is an odd integer." However, I am curious to know what logic would say about my definition for odd numbers.
I have a question about Video 31: Formal Definitions in Math| Ex: Even&Odd Integers. Why not all k that is an integer? Why must it be there exist another integer k?
Hey Trefor, thanks so much for all you do, I really appreciate your videos. I'm just wondering something...with these even/odd proofs, why are they in the form "there exists" instead of "all." Aren't all even integers n = 2k?
At 1:23, you used "if", why cant we use "if and only if"? Can we write it like " n is an even integer if and only if there exists an k such that n = 2 * k "? If there is a k that make 2*k = n then it means the n is even? It goes both way, no?
@@DrTrefor Thank you very much for making math very easy to understand. I try to practice along while watching your lectures. I came up with the answer before watching your video: "∀x ∈ D, ∃y ∈ Z such that x = 2*y +1. D is the set of all odd numbers." I didn't use "n is an odd number if there exists an k such that n = 2 * k + 1". Is my answer acceptable? Is it a matter of format? Do both answers mean the same?
Learning my entire course from this playlist. Infinite thanks Trefor🙏
My pleasure!
I'm learning this out of my own volition. Thank you for giving me access to higher-level mathematics. I'm starting to feel a love for math.
I can't thank you enough for making these videos! The professor for my class believes the students can learn this stuff just by working in groups and without the professor lecturing at all and it's NOT working for me. I failed my first exam and was debating on dropping out but you give me hope this may not be the end XD Thank you!!
Glad I could help!
Thank you so much for clarifying this! I'm currently taking this class at my University and my professor talked about this topic in a 6min video, which I did not understand. Watching your video... I finally understand.
Glad it was helpful!
Thanks a ton Trefor! Your playlist has helped me immensely in understanding the subject, to the extent that I have started admiring the concepts involved in it. You teach extremely well and lucidly.
🙏
You’re most welcome!
Wish more people watch his videos.
This is an awesome playlist! Thanks so much for putting this out.
Glad you like it!
Falling in Love with Math...Thank you Teacher
I'm so happy to hear that! Also, thank you so much for joining, I really appreciate that. Best of luck on your journey:)
I really appreciate this style of teaching.
What an amazing and helpful channel ! gonna ace my exam
What about this definition for even ints:
All x in Z such that x/2 in Z
Can we do that?
That would be fine.
@@DrTrefor Ah great, thanks. Although your definition seems to be more usable when doing further proofs.
thank you for putting this out exactly when my assignment is due . saved me, do u answer questions here?
Hello professor!
Do you think this would also conform to defining what an odd integer is(?):
n is an odd integer if ∃k∈ℤ|n=2k+1∨-1
I hope I get an answer from you
Thank you,
Punkrider
What would happen if we defined an odd integer as "an integer n1 such that, for some integer k and another odd integer n2, n1 = 2k + n2?" In logic, is there a term to describe definitions like these in which the thing we are defining is in the definition itself? This could, instead, be a proof for "the sum of an even and odd integer is an odd integer." However, I am curious to know what logic would say about my definition for odd numbers.
Your definition of an odd number relies on odd numbers already being defined so it doesn’t quite work
@@DrTrefor Thank you. Then, would the better proof be "the sum of an even integer and an odd integer is odd?"
I have a question about Video 31: Formal Definitions in Math| Ex: Even&Odd Integers.
Why not all k that is an integer?
Why must it be there exist another integer k?
Hey Trefor, thanks so much for all you do, I really appreciate your videos. I'm just wondering something...with these even/odd proofs, why are they in the form "there exists" instead of "all." Aren't all even integers n = 2k?
@@DrTrefor Got it, thanks for the explanation!
you're my hero trefor
haha thanks!
Why we don't define odd as there exists such integer k that n = 2k-1 ?
Or can we say
2k ± 1 ?
thank you very much sir!
At 1:23, you used "if", why cant we use "if and only if"? Can we write it like " n is an even integer if and only if there exists an k such that n = 2 * k "? If there is a k that make 2*k = n then it means the n is even? It goes both way, no?
@@DrTrefor Thank you very much for making math very easy to understand. I try to practice along while watching your lectures. I came up with the answer before watching your video: "∀x ∈ D, ∃y ∈ Z such that x = 2*y +1. D is the set of all odd numbers." I didn't use "n is an odd number if there exists an k such that n = 2 * k + 1". Is my answer acceptable? Is it a matter of format? Do both answers mean the same?
Is 0 an even number?
shouldn't "if and only if" be used in these definitions instead of just "if"? Just trying to understand the language :)