The Inverse Image of the Complement is the Complement of the Inverse Image Proof

[@dukeislam6293]

As an aspiring Mathematician whose grades are around 50/100 for the three-out-three class exams of the first series of proofing writing class of Undergraduate Mathematics (that’s a mouthful, run on sentences makes sense in mathematical proof writing, LOL, but not so much in English), I found this video inspirational. Seven days until the final exam for my Undergraduate Analysis course, now is the time I prove if I have what it takes to be a Mathematician. Thank you again for highlighting the beauty of mathematics.

[@rodbar87]

I just needed this justification for a probability exercise.

[@manongrygiencza8097]

Thanks a lot for your content! It helps me a lot and remember me why I do love Mathematics so much :)

[@joselukas24]

Can you show why this doesn't work for direct images? Thank You!

[@Fidder492]

As a first year undergrad in engineering, who skipped set theory but started straight into self-studying real analysis for fun, I'm glad I was able to prove the thumbnail before even watching the video. Though tbh, the inverse image / preimage of a subset and its definition was a really a hard concept to get around, like, holy moly, i thought I'd die jk. But technically the preimage of a subset A, denoted as f^-1(A), is just the set of all elements in the domain that is mapped to A under some function f if I'm not mistaken.

[@mammadmammadov499]

Thank you, Sir! I just wonder why you did not prove that the complement of pre-image is a subset of pre-image of complement? Is one direction proof enough in this question?

[@tig7965]

Thanks you sir

[@geetRH]

Thank you so much for your knowledge did share ☺️ it is helpful a lot 🙏

[@mattetor6726]

Im gonna work my way towards stocastic calculus :D Need to refresh the basics first!

[@TheMathSorcerer]

Nice 🔥🔥

[@nenanena8350]

Thanks 🙏

[@sambhusharma1436]

Awesome channel

[@TheMathSorcerer]

Thank you!

[@mattetor6726]

Thank you!

[@TheMathSorcerer]

🔥

[@demr04]

By the definition of logical bicondition x in h^-1(C) h(x) in C = ( (x in h^-1(C)) and (h(x) in C) ) or ( (x not in h^-1(C)) and (f(x) not in C) ) = x not in h^-1(C) h(x) not in C Can one prove like this?

[@LordOfNoobstown]

if we know the image is a function, does this in turn mean that the pre-image is bijective (at least i can not think of a way it can not be..)?

[@oscardavidalarcon2673]

Gracias por tus vídeos, los amo. I love Math.

[@TheMathSorcerer]

gracias amigo!! A mi tambien me encanta la matematica!! De donde eres?

[@oscardavidalarcon2673]

@@TheMathSorcerer Colombia

[@TheMathSorcerer]

@@oscardavidalarcon2673 awesome!

[@nelsonferreiraberg580]

Gracias por tus videos!

[@TheMathSorcerer]

👍

[@Hi_Brien]

The amount of notation in this random math video I decided to watch on a whim that I do not know is staggering. That thing that kinda looks like epsilon? What does that mean? {x>0| x} or whatever/however you use it? I've graded a paper where the answer key used that notation, but I don't think I've ever used nor learned how to read that. The subset thingy, I don't know what that is, I've seen a KZbin video where someone complained about an alternative way of writing that symbol and how it leads to unnessisary confusion. Do I know at all what it does? No, I do not. Have I ever seen f^-1 represented in that manner? No, I have not. Do I know what that x looking thing with a bar above and below it is? Not at all. But I'm not gonna mess with your watch time. If anyone can just drop a phrase I can look up to understand any of these things, I would appreciate that.

[@TheMathSorcerer]

Yeah it's a lot and in particular this one has things that are hard for people. Check out the first video in my advanced calculus playlist and the first one in my set theory playlist. Those go over some of this. Its pretty hardcore. Math majors struggle with this stuff at first.

[@TheMathSorcerer]

And its cool you are trying. My playlist on sets relations and functions has a bunch of similar proofs. If you see a definition usually not always it's explain Ed but yeah, takes tons of time to learn this stuff. I think it's great you started watching this as a random video haha so awesome 😀

[@pinklady7184]

I have never seen f^-1 before. It looks interesting.