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.
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
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.
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??
I have another video (Definition of a Function) that goes through all of the terminology. Unfortunately, some of the terms change depending on the branch of mathematics that you are studying, so it's not always so clear.
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.
Yes
Thank you for being so clear explaining maths.
Pls can it be concluded that, with surjective functions always the co-domain is the same as the range.
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
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.
This is an excellent video thanks a lot
Graph of e^x is above x axis.
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??
These are the steps:
Let y=e^x.
But then x=lny is a positive integer. So, g(x)=e^x(given)
(Implies) g(x)=e^(lny)=y.
Thus 'g' is surjective.
Why is e^lny equal to y?
So basically codomain is image?
I have another video (Definition of a Function) that goes through all of the terminology. Unfortunately, some of the terms change depending on the branch of mathematics that you are studying, so it's not always so clear.
Definition of surjection: f : A →B is surjective if ran(f) = B.
Nevermind, if you take the natural logarithms of both sides and equal them, you'll get that lny is lny. Thank you!
how to define f:z-->z
f(n)=3n
please help me
let function 'f' be the mapping of the integers to the integers defined by the set 'f(3n)' such that 'n' is in the integers
omg thank u so much!!!!!
No problem!