At 13:40... Must include 14 + 14 = 28 after 7 + 14 = 21. It is reasonable to first recur on the existing elements of S before taking into account the newly generated ones... Thank you for clear explanations!
That is not an error. There are multiple definitions for the natural numbers. One of those definitions includes 0 as the first natural number. That definition comes from the Peano Axioms. Look them up. They are interesting.
All sat frozen used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly watched denoting one or more people or things already mentioned or assumed to be common knowledge screen. Carry denoting one or more people or things already mentioned or assumed to be common knowledge pail identifying the person or thing affected or expressing motion in the direction of denoting one or more people or things already mentioned or assumed to be common knowledge wall used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly spill it in, at, or to that place or position. Paint denoting one or more people or things already mentioned or assumed to be common knowledge sockets in denoting one or more people or things already mentioned or assumed to be common knowledge wall dull green. Denoting one or more people or things already mentioned or assumed to be common knowledge clock struck identifying the person or thing affected or expressing motion in the direction of mark denoting one or more people or things already mentioned or assumed to be common knowledge third period.
Small typo at 4:17 , should be f(1 + 1) . Thanks for video!
OMG I caught that as well. Maybe this stuff is starting to click.
@@jamesvo5802 same bro took me almost 30 mins without checking the comments
That's why I was so confused lol thank you.
took me long time to figure it out, wish saw your comment before
Dude you saved me I was so confused lmao
At 13:40... Must include 14 + 14 = 28 after 7 + 14 = 21. It is reasonable to first recur on the existing elements of S before taking into account the newly generated ones... Thank you for clear explanations!
Thank you , this is very helpful for our final exam :)
Thank you so much for this video! My professor didn't go over this at all in class but still wanted us to do our homework on it :(
Yes he did
Shouldn't it be f(1+1) = ... at 4:16?
you're right. not f(1+2)
13:06
Here in this part could it be like if x belongs to s then x+x belongs to s
Doesn't natural numbers start with 1? The example that you gave in 12:15 is of whole numbers.
Depends on which camp you belong to.
I agree, natural numbers begin with 1, whole numbers start at 0.
Thank You Professor Kimberly You Are Awesome
@7:36 but why a^n is equal to a x a^n-1. So shouldn't a^n+1 = a x a x a^n-1 which is equal to a x a^n+1 ?????
Best explanation i've seen
Thank u.... But a small doubt...why 0 is added in the set of natural numbers.... N only starts from 1...
Mini Pramod This is the d version of the video. It is fixed on the new version.
That is not an error. There are multiple definitions for the natural numbers. One of those definitions includes 0 as the first natural number. That definition comes from the Peano Axioms. Look them up. They are interesting.
thank you sooooo much this very helpful!
perhaps my personal goat
Thank you so much for this! excellent presentation.
THANN YOU SO SO SO MUCH!!!
How on earth is 0 a natural number
Thankyou!!
thank you so much!!
i wish my professor was as good as you
Thanks 😊
Thank you! :)
Thanks for video
ASSASSINS!
Perfect
Thanks
Good Explained
KIMBERLY HELP ME I DONT UNDERSXTAND
This is terribly explained and some parts are just wrong like at 4:17.
You got 1 thing wrong, 0 is not a natural number. Natural numbers go from 1 to infinite. 0 is a whole number.
0 is taken as a natural number in discrete mathematics.
in my class, it includes zero
You miss spelled donut 9:23
You misspelt misspelled
fuck u
I know u are studying here nerd... I know ur here...
All sat frozen used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly watched denoting one or more people or things already mentioned or assumed to be common knowledge screen. Carry denoting one or more people or things already mentioned or assumed to be common knowledge pail identifying the person or thing affected or expressing motion in the direction of denoting one or more people or things already mentioned or assumed to be common knowledge wall used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly spill it in, at, or to that place or position.
Paint denoting one or more people or things already mentioned or assumed to be common knowledge sockets in denoting one or more people or things already mentioned or assumed to be common knowledge wall dull green. Denoting one or more people or things already mentioned or assumed to be common knowledge clock struck identifying the person or thing affected or expressing motion in the direction of mark denoting one or more people or things already mentioned or assumed to be common knowledge third period.
thank you so much!