Formal Definitions in Math | Ex: Even & Odd Integers

We've all seen even and odd integers before. But how - exactly - are they defined? How would you use them in a proof about the even, and odd integers. In this example we properly define the even and odd integers. In the next video, we will use them in a proof about even and odd integers.

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[mrqlsql]

Learning my entire course from this playlist. Infinite thanks Trefor🙏

[armandoapolinar]

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.

[FlyingTigerRabbit]

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!!

[sammy_vee]

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.

[arkaseth]

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.

🙏

[theritesh]

Falling in Love with Math...Thank you Teacher

[Wildwildmint]

I really appreciate this style of teaching.

[FlutterDev]

This is an awesome playlist! Thanks so much for putting this out.

[lucianasalas]

What an amazing and helpful channel ! gonna ace my exam

[boogaloobomber]

What about this definition for even ints:
All x in Z such that x/2 in Z
Can we do that?

[punkrider]

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

[pedramhaqiqi]

thank you for putting this out exactly when my assignment is due . saved me, do u answer questions here?

[kingwoomy]

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.

[JJ-ckiy]

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?

[Ashley-yrky]

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?

[drzewo]

Why we don't define odd as there exists such integer k that n = 2k-1 ?
Or can we say
2k ± 1 ?

[bluejimmy]

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?

[jumpydino]

shouldn't "if and only if" be used in these definitions instead of just "if"? Just trying to understand the language :)