Thank you! Here is a proof that the composition of injective functions is injective, which, together with this video, completes the bijective proof. ruclips.net/video/yQF8WiQnWLE/видео.html
Thanks for watching and for the question! We use "onto" to mean "surjective". I think of "onto" meaning "surjective" because a surjective function A to B, in a way, places A 'onto' B entirely covering B, since every element of B is mapped to by some element of a through f. We use "one-to-one" to mean injective, but we have to be careful there because sometimes a similar phrase "one-to-one correspondence" is used to describe a bijection. Ultimately, I think it's best to use injection, surjection, and bijection.
The input of f is B, which outputs only C. So, if you tried to to do g o f, you'd be taking the output of f (which is C), and inputting it into g. However, the input of g can only be A.
I CAN'T THANK YOU ENOUGH FOR THIS VIDEO!!
You're very welcome! Thanks for watching and let me know if you ever have any questions!
can someone Please share the video that he mentioned about the converse of this proof, and thanks a lot really it helped me a lot in my studies
Thank you for the very helpful video♥️
Thank thank thank you so much
My pleasure, thanks for watching and let me know if you ever have any questions!
@@WrathofMath super thanks when I am in trouble I should really ask😅
This was extremely helpful! You're such a good teacher! Could you do a video on showing the composition of bijective functions is bijective?
Thank you! Here is a proof that the composition of injective functions is injective, which, together with this video, completes the bijective proof.
ruclips.net/video/yQF8WiQnWLE/видео.html
You are a life saver!
Glad to help, thanks for watching!
hello.. is it onto or one to one which called as surjecttive?
Thanks for watching and for the question! We use "onto" to mean "surjective". I think of "onto" meaning "surjective" because a surjective function A to B, in a way, places A 'onto' B entirely covering B, since every element of B is mapped to by some element of a through f. We use "one-to-one" to mean injective, but we have to be careful there because sometimes a similar phrase "one-to-one correspondence" is used to describe a bijection. Ultimately, I think it's best to use injection, surjection, and bijection.
thanks a bunch!!
Glad to help! Thanks for watching!
Is f of g is similar to g of f?
Thanks for watching and what do you mean? They're not necessarily equal, nor are they both necessarily defined. What do you mean by similar?
@@WrathofMath I think he is asking if the proof holds for g o f as well. (i.e. if f and g are both surjective, is g o f also surjective)
do you have one that proves that the Composition of injective Functions is injective
Yes, here it is! ruclips.net/video/yQF8WiQnWLE/видео.html
can anyone explain what x prime means
in this case its just some notation he could have used anything i.e., x1, x* ...
Why is it f o g? I shouldve been g o f
The input of f is B, which outputs only C.
So, if you tried to to do g o f, you'd be taking the output of f (which is C), and inputting it into g.
However, the input of g can only be A.