Direct Image of Union of Sets Proof: f(A U B) = f(A) U f(B)

[@Goose____]

man singlehandedly saving me from failing algebra, thank you

[@whisperofspring]

Now that I know how to do it, I feel really stupid for not getting there on my own. You helped me a lot. Thanks!

[@TheMathSorcerer]

yay:)

[@pez4]

Who else is here in 2020?? Thanks from Mexico, Math Sorcerer! :D

[@TheMathSorcerer]

you are welcome!

[@j.m.e.1326]

Thanks from germany too

[@manuelkarner8746]

Thanks from Austria (not Austraila lol) toooo for being ouer Math-Gandalf

[@cannydou3187]

Yes there is someone out there who needed this...thanks wholeheartedly for this!!

[@PaulPaul-kf8sn]

Greetings from Germany :) Thanks so much for the video. It helped me a lot with my first homework at university!!!

[@dayvisons01]

Thanks, from Brazil

[@genshingeek1375]

Wow you help me a lot with my homework Thank you :))

[@TheMathSorcerer]

:)

[@arzylannamchyl880]

Thank you very much, from Russia, Novosibirsk State University

[@TheMathSorcerer]

Wow Russia!! Very cool! You are welcome 👍

[@TheScawer]

Oh sweet! Just what I needed, thank you. :)

[@TheMathSorcerer]

np:)

[@SunnyKumar-bh6te]

I am indian but this videos are very helpful

[@walida.1111]

thank you so much !! , you're really good at explaining.

[@acdude5266]

What is the software you re using with the black background and fluorescent markers? Thanks!

[@TheMathSorcerer]

Smoothdraw

[@andresescobar1616]

Amigo. En realidad no puedes finalizar de esa manera la demostración. Tienes una proposición de la forma PvQ y simplemente comcluyes P. Lo que haces con la promera proposición tienes que hacerlo con la segunda para que te quede de la forma PvP. Aun asi esta bien lo demas, solo falto el final un paso. Gracias ❤

[@TheMathSorcerer]

[@howardcheung8304]

Thanks from Hong Kong

[@TheMathSorcerer]

Wow Hong Kong ! Super cool😎😎😎

[@shivaprasadbs6266]

thank you so much sir ...send the more video about real analysis sir

[@inioby3904]

thank youuu 🙏🏽🙏🏽

[@julianhautzmayer2232]

Thanks from Austria!

[@TheMathSorcerer]

Glad it helped!!

[@woid0]

tug gang

[@jonas7438]

Why am I not done at 3:50 ?? I just don´t get it. Can someone help me out?

[@joevanvaler392]

By 3:50, we have only shown that f(AUB) is a subset of f(A)Uf(B) (meaning, anything in f(AUB) is in f(A)Uf(B)), but we have not shown that everthing in f(A)Uf(B) is in f(AUB) yet, or in simpler terms, that f(A)Uf(B) is a subset (or contained within) f(AUB).

[@angadvishwakarma35]

How to prove any function as injective if it's inverse is given?

[@abdellatifdarmellah]

thnks from algeria

[@TheMathSorcerer]

you are welcome!

[@ronakroy6622]

Thanks for helping...

[@david_ga8490]

Thank you so much. BTW, it's fun to look how the typical abbreviated expressions like such that, without loss of generality, ... change through languages: In English it's st, wloy... In Spanish we use tq, spdg... XD

[@TheMathSorcerer]

tq = tal que? what about spdg? What is that in spanish? Thanks:)

[@david_ga8490]

@@TheMathSorcerer yeah tal que The other one is sin pérdida de generalidad, but I haven't actually seen it abbreviated...

[@nadamerraka5660]

i am so grateful 😊tnx

[@TheMathSorcerer]

so glad this helped someone!

[@НастяБазюк-ф1к]

Thank you!

[@TheMathSorcerer]

np!

[@Freedan14go]

[@abdellatifdarmellah]

u the best man

[@TheMathSorcerer]

thanks man!

[@Shkencetari]

Thanks.

[@TheMathSorcerer]

+Shkencetari np!!

[@grimgirl283]

Thanks! I hope you're still making math videos to help dumb college kids like me! XD

[@TheMathSorcerer]

Ya of course😀