(Abstract Algebra 1) Surjective Functions

The definition of surjective (onto) functions is given along with an outline of how to prove that a function is surjective.

[jeffwilken]

Your examples of injective (previous video) and subjective mappings are identical, which sorta obfuscates that they are two distinct ideas. Would’ve been helpful if you’d given non-bijective examples to highlight the difference. Just a minor quibble! In any case, I appreciate you taking the time to make these.

[saralopez]

Thank you for being so clear explaining maths.

[fmikael]

So just a clarification between Injective Vs Surjective - The former states that every element of A has a one to one mapping, with an element in B. Whereas surjective means that every element of B has a mapping to A, this would mean that multiple values of A can map to the same value of B

[yakopro]

This is an excellent video thanks a lot

[juanjaimescontreras]

Great video like all the rest of your videos. Question based on the DEF: let y be from R+
then y = e^x, for some x from R. is this different from your proof on step 2:
G(ln y) = e^(lny) = y??

[kingsleyblay]

Pls can it be concluded that, with surjective functions always the co-domain is the same as the range.

[TeeMee]

Don't really get why those proofs work. You find one example of an input that maps to one output, but you have to check every output. You'd be able to prove it's not subjective by working out the inverse of the function and finding a counterexample inverse function input that does not produce a defined result.

[marcdamian]

Nevermind, if you take the natural logarithms of both sides and equal them, you'll get that lny is lny. Thank you!

[maxpercer]

Definition of surjection: f : A →B is surjective if ran(f) = B.

[helpdeskjtmk-]

how to define f:z-->z
f(n)=3n

please help me