How to Prove Math Theorems | 1st Ex: Even + Odd = Odd

Our first math proof! The main goal of this video is more about the structure of a direct proof than the specific claim, that the sum of an even integer and an odd integer is an odd integer. We will write:
1) The Assumptions
2) Definition of the Assumptions
3) Manipulations
4) Definition of Conclusion
5) Conclusion

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YOUR TURN! Learning math requires more than just watching math videos, so make sure you reflect, ask questions, and do lots of practice problems!
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[tianhaowang]

His eyes are shining when he is explaining how to prove this problem. very clear explanation

[smaelss]

You know you've got it right when the YouTube algorithm gives up, and start recommending some great content.
thank you, Sir

[Khalidnk]

I'm currently in my first term in Grad school, and really struggling to understand the mathematical proof due to my week background in math. These videos really helped me! Thanks a lot

[zealous]

Dude, my god!! I’m genuine in saying this was brilliantly taught.

I’ve tried two proofs prior to this video, and I seemed to be very good at coming up with the steps to prove my theorems but struggled with structuring the proof. This video was everything I needed for learning how to properly structure my direct proofs!

And to repeat myself with elaboration, I truly believe the way you introduced + developed concepts was extremely beautiful. I had a very, very high level of enjoyment on this vid. Never fail to deliver, which is why you earned my subscription a while back

[ptree]

I was pretty lost on this concept until I studied this video. Thank you.

[arikayemusic]

I joined discrete math really late into the year and your videos are saving me! Much love :)

[mrcookies]

You are incredible Professor, I have learned so much from your videos you have no idea!

[ambassador_in_training]

Thank you very much professor Trefor for sharing such a wealth of knowledge in a very user-friendly way. The Feynman technique is surely a strength in your teacher's toolbox.
God bless you richly for allowing many aspiring math students to have hope of doing well in mathematics.

[bralenmartin]

Thank you for demolishing my belief that an even plus an odd could be even....

[eduardorivera]

God I wish these videos existed when I took my Discrete math course. So CLEAR!! Either way, it's nice to watch!

[TheValorArtz]

This is awesome. Will you be doing more proofs. Looking forward to them if you are

[anastasiarose]

Love your videos. Learning so much from them.

[mdforbes]

Isn't this conditional derivation instead of direct? Maybe set theory has different terminology than classical logic, but an assertion of P -> Q. you assume the antecedent and try to show the consequent. Still, an excellent example. Really enjoying your series.

[TheRedPython]

Do we need to prove that;

1) there is no number that is both even and odd

and

2) an integer plus and integer equals an integer?

[pes]

Shouldn't the proof for odd be n= 2k-1 to accommodate the integer n=1?

[jordainegayle]

so could we say the sum of odds give an even? how can we prove that?

[adnanmustafa]

Sir ager urdu mn expalin karain to koi masla nai ho ga
Ap ky video achii lagy kafi sumjh aye ha

[yallowgaming]

I m from pakistan but your teaching skells are unbeliveble keep it up sir good job

[BloxxingDinosaurus]

"Manipulation" sounds so negative, it's like you are gaslighting people with lies to make them believe you.

[HaldaneSmith]

This video should have been about two minutes long. The teaching was in the example and the long-winded explicatuon wasn't necessary. More examples would have been a much better use of time.