Please help with injective, surjective and bijective functions

[blissful hazel]

1. My attempt on solving injective and surjective function.

[vital monolith]

that works ig

it's the identity function

[blissful hazel]

So what do I do with task 2? 🥲

[vital monolith]

you can also do map for a=1..4, a->a+1, but 5->1

[vital monolith]

another word for surjective is onto

[blissful hazel]

Onto?

But the second one isn’t supposed to be surjective at all, I thought?

[vital monolith]

oh sorry i misred

but still

[vital monolith]

that means that your whole codomain is "covered"

if you make a function that just leaves out for example 5

i.e. nothing maps to 5

[blissful hazel]

So for example

Like this?

[vital monolith]

no

[blissful hazel]

Oh

[vital monolith]

nothing maps TO 5

there can be some map from 5

[blissful hazel]

But doesn’t it do that in the picture? Or do I misunderstand

[vital monolith]

^

you can't leave anything out from the domain

what's the definition of an injective function?

[blissful hazel]

Also called a one-to-one function?

Like each unique input maps to a unique output but I thought that’s exactly what I did

[vital monolith]

yes but you left out 5 in the domain / image

in your function, f(5) is not defined

and it should be

[vital monolith]

and your unique input belongs to A

which includes 5

[blissful hazel]

So how is this any different from bijective then

[vital monolith]

consider this map

1->1
2->2
3->3
4->4
5->4

[vital monolith]

also no, that's wrong

i just realised

injective is
if a=b, then f(a) = f(b)

it doesn't say that they have to be unique

[vital monolith]

your definition is for bijectivity

[blissful hazel]

Okay to get this straight, this is correct?

[vital monolith]

yes

that is bijective

actually

i just realised it says "partial function"

okay i am sorry about the second one

[blissful hazel]

Where does it say that?

[vital monolith]

this looks correct

[blissful hazel]

Oh I also didn’t realize

[vital monolith]

in the task

oops

[vital monolith]

this is correct and you can leave out 5 in the domain because it's a partial function

[blissful hazel]

Oh why is that?

So {1, 2, 3, 4, 5} is the range and it doesn’t need to cover each and everyone?

[vital monolith]

yes because it's a partial function

[blissful hazel]

Ahhh

[vital monolith]

from wikipedia

[blissful hazel]

My examples seem too easy for it to be correct tho

😧

[vital monolith]

i mean they are techinally correct

you can swap around a couple of arrows and it will still be fine

[blissful hazel]

Hmm alright

Thx!!