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ur the goat

Your notation seems pretty straightforward. It made me think about what the empty composition is if it exists because I recall that if you take the product of an empty set you have 1 which is the multiplicative identity and if you take the sum of an empty set you have zero which is the additive identity. This makes me think that there must be some function g such that f ◦ g = f but if we expand the equation, f(g) = f(x). This leads me to believe that the empty composition is the identity function g(x) = x.

This is a cool way to understand the theorem with abuse of notation.

Thanks it was a good proof ❤

You should've mentioned that the set of bounds are the roots of the function otherwise the equality doesn't always hold.

Perfect explanation, thank you for making this, saved me having to explain this concept to a first years bachelor student.

I think we can all agree on what aleph null means

thanks, i randomly had this thought in my head lol

damn you cleared my doubt , thank you!!

Thanks too much!

Really helpful. Thanks!

Yo during the part about rotating the levitating half circle around the x axis I’m not sure the formula is correct. Shouldn’t it be the integral of s1^2 minus s2^2 ?

Y R U SO GOOD AT EXPLAINING OMGGG 😭😭🙏🏻

simple and easy. like it

Bro im just now watching these videos and this guy is awesome at helping conceptualize this unit. U def saved my grade, thank u sir

bros the goat🐐

Spent the past month on this unit in class and understood nothing. 25 minutes here have clarified everything excellently. Thank you!

Just found your channel and you have taught me more than my teacher has taught me the entire year!! Thank you so much!!!

Thank u really much for these videos!

Don't stop. Your work only compounds. Keep working on things that you find interesting!

good.vid

I've seen a bunch of people who make sigma like an opposite 3 😂😂

So basically its least and greatest integer function

I am the "K" one 😂😂 But I first make the horizontal bar then make the lower portion

Thanks for contribution 😊

This is so sad, i just came across your channel 3 days ago, that was 1 night before my Applications of integrals test☹️. Your video helped me so much i dont even know how to thank you for that. I hope you come back to posting yt videos soon'

While I am writing this before the video is even published, thank you for your contributions to online math education. I especially appreciated how your videos were very accessible to those with little background on a topic, or otherwise introduced problems which delved into greater depth than often taught in school. Best wishes for the future.

for continuity, isnt there a theorem that say that the lim f(x) has to be equal to the functions value at that point. So, perhaps thats the reason why its defined also at the endpoints? Great video btw. Thanks!

we need a new letter for speed, because s is already used for position

Perfect explanation. I liked it

Great video

goat

over here we call it the sandwich theoerem :D

Thanks this really helped!

Thanks alot!

The easiest questions to ask 8-year-old children in Turkey:

How should I take notes from math books?

Intriguing

so all monomial that has h will be 0 and cancelled out as h approaches 0? . i was stuck on what to do with those monomials with the H. lmao

🤓

Wonderful video

Ok that was easy

Why not use epsilon delta definition of continuity to prove it ?

You should rewrite f(c)g(c) as (f*g)(c) and the inside of the limit as (f*g)(x). As a function isn't the f(x), it's the f; f(x) is simply used to denote the image of an arbitrary object, x.

Hi bro where are you belong from 😊