Injective Functions (and a Proof!) | Injections, One to One Functions, Injective Proofs

[@leeming1317]

My asnwer: I would say no because if x is a negative number then it maps to the same number of its positive counterpart, thus the function does not preserve distinctness

[@klarapolzl5776]

Absolutely love the videos! keep the great work up. you deserve much more subs! would love to see more proves on maybe a little harder surjective, injective and bijective functions

[@WrathofMath]

Thank you for watching and for your kind words! I'd be happy to do more proofs involving those various types of functions. Do you have any particular in mind you'd like to see? If not, I'll try to come up with some lessons in the coming weeks. I'm behind on viewer requests right now unfortunately, but I plan on getting to them all!

[@fuscabloangelo9511]

i got it when you plug in numbers instead of putting letters like x it makes me confusing thank you it's really helpful because there's so many tutors in youtube but i find it confusing until one time i watch your videos it makes me a lot easier

[@WrathofMath]

So glad it helped! Thanks for watching and let me know if you ever have any questions!

[@leeming1317]

Thanks for this lesson, I stopped at this section before I went to bed and was like OMG jeeeze, but this made reading that section a lot easier, It was just like symbols and new words everywhere! haha

[@leeming1317]

3:04 Also, if one of the elements in A mapped to something outside of B it also wouldn't be injective anymore right?

[@leeming1317]

5:25 It isn't injective because the function maps to the same number once, making it not longer distinct, or one-to-one?

[@nononnomonohjghdgdshrsrhsjgd]

Hi, your videos are very helpful. Are all videos organized in playlists? In which playlist can I find this for example? I wanted to watch the whole series in which the concepts bijective, surjective, injective are explained. I counted the number of videos and the number of videos in the seperate playlists, and it looks as if there are more videos seperately than videos, organised in playlists? Can you put a link in the description below the videos or in the title, or anyhow make it possible to choose the whole playlist, once we find a video, we are interested in. Thank you very much!

[@neaworld3960]

Jesus loves you! Please repent of your sins today

[@nononnomonohjghdgdshrsrhsjgd]

@@neaworld3960 you are insane

[@kazusensei7514]

Hello can i ask how did g(-3) became g(3) in 5:19

[@sennadl8602]

Bc its an absolute function so - doesnt exist

[@MugisaJoseph-uf5sz]

but sir it seems the proposition dimension is not independently efficient to prove injection Both proposition and contrapositive should be used concurrently

[@amiheretv8318]

F(x)=3x^2 F(-x)=3(-x)^2 F(-x)=3x^2 since F(-x)=F(x) 3x^2=3x^2 Then f is injective 3x^2=3x^2

[@namehere2986]

f(-x)=f(x) therefore f is NOT injective

[@lucien_x2]

f(x) = f(y) 3x² = 3y² x² = y² ±x = ±y includes case +x = -y x =/= y ∴ f(x) = 3x² is not injective

[@s_b_r_2000]

Nice work.. thanks...

[@WrathofMath]

You're welcome, thanks for watching!

[@jayantpathak5477]

Sir it is not injective as -3 isn't equal to +3 but their images are... Hence defying the contrapositive

[@WrathofMath]

Thanks for watching Jayant and good work, that's exactly right!

[@giftmapote1865]

@@WrathofMath Hi Sir...but i don't understand because if we assume that f(x) = f(y) >>> 3x^2 = 3y^2 then we divide by 3 and find square roots both side then we will be left with x = y.....doesn't that mean its injective

[@joblo1978]

@@giftmapote1865 NO, because x is not equal to y. The simplification results +/- x = +/- y, which can't always be true, so it's a contradiction assuming x = y. Also, we know that 3x^2 is not one-to-one via the horizontal line test.

[@leeming1317]

0:55

[@benjaminw.2838]

if x!=0; x != -x ...(a) ; However, 3(x)^2 =3(-x)^2 -->f(x)=f(-x) ....(b); based on (a) and (b) --> f(x) is not injective

[@paulhammond6978]

f(x) = 3 x^2 is not injective since f(-1) = 3. (-1) (-1) = 3 = 3. (1). (1) = f(1).

[@aboutfargona4285]

i got the answer right

[@WrathofMath]

Awesome, good work! Thanks for watching and you might be interested in this new lesson proving a bijection: kzbin.info/www/bejne/gZWmnaOkjsd6Zqs

[@benemmanuellepacunla6743]

Hi

[@WrathofMath]

Hi Ben! Thanks for watching!