Professor Brehm, I think you should get 50% of the tuition money I paid for my university because you've saved my life in Linear Algebra and now Discrete Maths! Thank you for these videos, I am forever grateful :))))
Im a college freshman majoring in CS and really struggling in Discrete Math rn. U just saved my life because this well-explained things right here. Thank you
I have followed your playlist video for a while now and am currently on video 13th. I gotta say, your video are very easy to understand and teach me so much. I'm not at Uni yet, but will be after this summer break, and I'm watching this to prepare.
There exists a real number x such that for all real numbers y such that x is not equal to -y. This is FALSE because x=-3 , -y=-3 -3=-3 IS MY EXPLANATION CORRECT?
I kinda wonder at timestamp 11:15 statement number 3 where there's an existential and universal quantifiers nested together such that x*y=0. I think the statement should be false because the existential quantifier defines there exists at least one object in the domain that satisfies the conditions which is not true because there's only exactly one x which is equal 0 to satisfy that condition.
"at least one" is satisfied even if there's exactly one. it's the same as saying that the amount of values that satisfies the condition is greater than or equal to 1. You would be right if the quantifier meant "there is more than 1," because that statement implies that one is unsatisfactory.
In the 2nd example you say the existential y value can change but I thought you are only suppose to use 1 value for "there exists" not change them to accommodate " all x's"... a bit confused about that 1
The last statement is saying "there exists an x, where with a corresponding y, x/y=1". Because of this, you only need one example to deem the statement true. One example where a certain x and y value makes the equation incorrect doesn't make the overall statement false because of the "there exists" clause on both variables. As long as one example proves the equation true, nothing else matters, the statement is true.
@@ObadiahHoss thanks for ur explanation. So if there is two existensial on a variables, as long as we prove it true by one statement, so its true, eventhough we have a counter-example like the cases in the video.
Can we interpret , for all x there exist y as a many to one function from x domain to y co domain , and there exist y such that for all x as a one to many function form x domain to y co domain .
Professor Brehm, I think you should get 50% of the tuition money I paid for my university because you've saved my life in Linear Algebra and now Discrete Maths! Thank you for these videos, I am forever grateful :))))
This is an amazing instructor. Everyone can learn discrete mathematics from this instructor. May you continue to teach for another 100 years.
Im a college freshman majoring in CS and really struggling in Discrete Math rn. U just saved my life because this well-explained things right here. Thank you
did you pass the whole course with her videos?
@@Daniel-nm6pfHer lectures are brilliant. Go for it without a second thought, you won't regret it.
Did you pass??
Yes. All A so far
Yep! 3 weeks in and I finally decided to look for help on CZcams. Thank god I found your channel. Thank you so much, life saver.
my final 2 days
Your new explanation of x/y = 1 is much better in this video. I hope your twins are doing well!
You are her real life student?
I have followed your playlist video for a while now and am currently on video 13th. I gotta say, your video are very easy to understand and teach me so much. I'm not at Uni yet, but will be after this summer break, and I'm watching this to prepare.
Awesome! You will be way ahead of the game!
Hello, I am currently doing the discrete mathematics class in computer science and I just wanna say that your channel is a gem. Thanks a lot
this is well explained. Im currently a undergrad Computer Engineer and this video actually helps. Thanks!
WHY ARE YOU SO GOOD AT EXPLAINING!!!! i wish you where my professor!
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This is so great it’s just like my class but I understand this version.
i finaaaally feel like my ass has been saved . thankyou so much for such fantastic explanation
Finally I get this point, you are awesome thank you.
Thanks for this amazing course!
You are a much better Instructor compared to my prof
Thank you Thank you Thank you.
Wouldn't it be more correct to use the uniqeuness quantifier for "Every real number has an additve inverse" since they each only have one?
your actuallt amazing. i love u
There exists a real number x such that for all real numbers y such that x is not equal to -y.
This is FALSE because x=-3 , -y=-3
-3=-3
IS MY EXPLANATION CORRECT?
For Example 1, would it be allowed to say that the P(x,y) is a tautological function? Since xy=yx is equivalent to 1=1, which is always true.
for the negation question what would be the truth value for that question ?
I kinda wonder at timestamp 11:15 statement number 3 where there's an existential and universal quantifiers nested together such that x*y=0. I think the statement should be false because the existential quantifier defines there exists at least one object in the domain that satisfies the conditions which is not true because there's only exactly one x which is equal 0 to satisfy that condition.
"at least one" is satisfied even if there's exactly one. it's the same as saying that the amount of values that satisfies the condition is greater than or equal to 1.
You would be right if the quantifier meant "there is more than 1," because that statement implies that one is unsatisfactory.
In 14:05, why can Ey change for any number Ax when the opposite cant be done?
you make it seam so simple
In the 2nd example you say the existential y value can change but I thought you are only suppose to use 1 value for "there exists" not change them to accommodate " all x's"... a bit confused about that 1
Thank you.
15:09 for the last example wouldn't it be false? because x and y could have both been 0 and 0/0 is not equal to 1.
The last statement is saying "there exists an x, where with a corresponding y, x/y=1". Because of this, you only need one example to deem the statement true.
One example where a certain x and y value makes the equation incorrect doesn't make the overall statement false because of the "there exists" clause on both variables. As long as one example proves the equation true, nothing else matters, the statement is true.
@@ObadiahHoss thanks for ur explanation. So if there is two existensial on a variables, as long as we prove it true by one statement, so its true, eventhough we have a counter-example like the cases in the video.
Can we interpret , for all x there exist y as a many to one function from x domain to y co domain , and there exist y such that for all x as a one to many function form x domain to y co domain .
can someone give a further explanation for the first example pls?
what if y = x ?
7:40 cant u let y = 5- x and then for any x it is true?
or x = y
Cooool
What is the software that you use for writing?
I'm just using Microsoft power point and the recording tab.
Thank you👍🌷
15:12
🅝🅘🅒🅔
Chup mahgya