The Definition Of A Function | Different Types Of Functions | Injective, Surjective and Bijective

TheMathCoach explains the fundamentals about functions. The video covers: The definition of a function, Sets, Domain, Codomain, Range, Injective (one-to-one) functions, Surjective (onto) functions and Bijective functions. There are examples included for each concept, to help clarify it while allowing the viewers to test their new knowledge.

Consider subscribing and liking if you enjoyed this video or if it helped you understand the subject. It really helps me a lot.

CONCEPTS FROM THE VIDEO
► Function:
A function relates each element in a set to exactly one element in another set and is a powerful tool to use, when we want to test situations out on paper before we do it live. The notation used: f(x) or f: X -- Y

► Set:
A collection of distinct objects, also called elements.

► Domain:
The set that the function relates elements from.

► Codomain:
The set that the function relates elements to.

► Range:
The set that contains all elements that the function relates to in the codomain.

► Injective - one-to-one function:
A function that never relates two distinct elements of its domain to the same element in its codomain.

► Surjective - onto function:
A function that have to relate to all the elements in the codomain and can therefore relate to the same element in its codomain infinite amount of times. Another way to say it is that the range/image is equal to the codomain for the function.

► Bijective function:
A function that is both Injective and Surjective.

TIMESTAMPS
Introduction - 0:00
What is a function? - 0:20
Definition of a function - 5:38
Function or not? - 6:59
Different types of functions - 8:38
Which type of function is it? - 10:37

ISSUE WITH AUDIO
I am sorry about the drop in audio quality in some parts of the video. I did not have time to fix it and I hope you can manage.

SOCIAL

SOURCE
► Diskret matematik och diskreta modeller, (2002), Kimmo Eriksson, Hillevi Gavel
► Analys i en variabel, (2001), Arne Persson, Lars-Christer Böiers

[janoambitious]

Awesome! very clear explanation. Hope you make some videos about sets and proofs.

[ensarb]

You’re awesome dude, I finally understood them. Keep it up and thanks for the free class

[gayathriayyala]

Thank you really much sir. It helped a lot. :) Please keep updating us more and more.

[yxoozo]

Great video! And the Swedish accent makes it even better :D

[kalsoomasghar]

Thank you so much. It was very clear and well made.

[janoambitious]

thanks for your reply. It would be very nice if you cover set proofs in your video.

[qsnowboard]

MMMAAANNNN!!!! YOU ARE FU*KIN GOOOOD! MAKE MORE VIDEOS!

[shynyjacob]

Sir let me ask u a doubt.... In an example u put up to distinguish between function and non function the second mentioned is many one function and u said it as a non function.... Why?

[sabinaixchelgarciamendoza]

the example of surjective doesnt contradict the def. of function???

[muazhassan_]

thank but one to one function was missed

[_singh_m]

you talk really slowly and beat around the bush