Disproving implications with Counterexamples

[@nabeelkhan717]

You are teaching same topics as my instructor but I can't understand a single word from his lectures until I have watched your videos. Thank you for saving me ❤

[@kaikleinbard7544]

your videos are so helpful and clear - THANKS!!

[@doomteam12345]

Can I get a heart for watching all of your series?

[@doomteam12345]

Trefor Bazett honestly your videos are great. I watched your whole series for my discrete mathematics class. I then went through my book and had a good understanding of everything so I was able to quickly go through it. Only suggestion I would make is for the harder things to remember, make a 2nd video with about 1-3 examples.

[@andyjiang5809]

How do you write backwards so effortlessly?!

[@DrTrefor]

I spent years practicing. Or, i use the computer to do a mirror image. One of those:D

[@amckeetrades]

@@DrTrefor P v Q therefore True

[@robbiemayer3573]

I wish I had your enthusiasm :)

[@ypleong02]

This helps me a lot, thank you so much...

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[@coregidormariajesleye.7356]

Thank you so much, Dr. It helps a lot.

[@suhailawm]

tnx alot sr. im 4m Sri Lanka

[@study-y7t]

when the domain is (Z+) the statement is always true or not ?!

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[@christopherbarrett9900]

Love it!

[@Regnad1]

Thank you😢

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You the man

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[@kayekayralynvillanueva4856]

|x|>0 disprove this using counterexample

[@thegeneralgamer4921]

|0| is not greater than 0 A tip when doing counter examples, try to always think of the less thought of numbers. For example, the obvious numbers would be 5, -10, 200, etc. But I immediately knew this was 0 because 0 is neither negative nor positive, and is not affected by absolute value. This makes 0 kind of a misfit or odd case, in which it can (and did) 'break' the theorem by proving it wrong. Also always test 0 if possible because 0 usually seems to be problematic a lot of the time lol