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anonymous
 one year ago
plearse teach me injective, surjective and byjective
anonymous
 one year ago
plearse teach me injective, surjective and byjective

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zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Do you know what a function is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you are given variables and replaced by numbers for short

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2A function is onetoone (injective) if every x in the domain maps to at most one y in the codomain example dw:1441760363692:dw here is a non example dw:1441760400010:dw Does this make sense?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2notice that in the first picture each element in the domain (the one on the left) gets sent to only one element on the right (this is the codomain) Notice this is NOT the case in the non example

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. so the first is injective?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2the second one is not because 1 and 2 both get sent to a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in any function, every x maps to at most one y in the range

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2A function is onto (surjective) if everything in the codomain gets used up example dw:1441760739646:dw non example dw:1441760788586:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0read this http://www.math.ucla.edu/~tao/java/MultipleChoice/functions.txt

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0" For every x in X there is at most one y in Y such that f(x) = y." Comment. Every function f has this property (they each map one element to one element, i.e. they are not "onetotwo"). However, this is not what onetoone means.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2A function must have 2 properties 1) it is defined everywhere i.e. everything in the domain gets used up notice how surjectivity is sort of like the opposite of this 2) it is well defined i.e. each x can map to at most one y notice how injectivity is the opposite of this

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Ok @GIL.ojei Is the following function surjective, injective both, or neither? dw:1441761073116:dw ?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2@jayzdd I think it is much better to start with a intuitive notion. this notation is not going to help imo. that comes next

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a better definition for injectivity distinct (different) inputs map to distinct outputs formally: if a ≠ b, then f(a) ≠ f(b) this is equivalent to if f(a) = f(b), then a = b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes you're diagrams are good to explain the intuition. i was taking issue with the phrase 'every x has at most one y ' for your one to one thats true about all functions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because each maps differently and are all exhausted in the left

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2because each maps differently, is why it is injective The fact that each gets used up is actually a property of it being a function.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Ok @GIL.ojei is it surjective

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0gil no two x values map to the same y value. agreed?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2OK @GIL.ojei is it surjective?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2remember that surjective just means that the entire codomain (the circle on the right) gets used up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because no single element of X mspd to two elements of Y

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2what you just said is true of all functions

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2It is injective because no two x elements get sent to one y value It is surjective because every element in the codomain gets used up

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2ok so when it is both surjective and injective we call it a bijection.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Here is what is important, and here is the notation that we use A function \(f:D\rightarrow C\) is a relation with the following two properties. 1) \(a=b\implies f(a)=f(b)\) 2) \(\forall x\in D\) it is true that \(f(x)\in C\) A function is surjective if \(f(a)=f(b)\implies a=b\) where \(a,b\in D\). A function is surjective if \(\forall y\in C \ \exists \ x\in D\) such that \(f(x) = y\). A function that is both surjective and injective is called a bijection.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Now think about why these things are saying what we talked about above.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2@jayzdd pointed out, in my very first post I should have said injective implies no two domain elements map to a single codomain element

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok buy i do not understand this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A function \(f:D\rightarrow C\) is a relation with the following two properties. 1) \(a=b\implies f(a)=f(b)\) 2) \(\forall x\in D\) it is true that \(f(x)\in C\) A function is surjective if \(f(a)=f(b)\implies a=b\) where \(a,b\in D\). A function is surjective if \(\forall y\in C \ \exists \ x\in D\) such that \(f(x) = y\). A function that is both surjective and injective is called a bijection.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2Ok well lets talk about the surjective surjective says that no two different domain elements can map to the same y value, so if two things map to the same y value they better be the same thing in other words \(f(a) = f(b) \implies a=b\)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2does that make sense?

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2The reason we are going over this part is because you are going to be asked to show a function is surjective and injective and this is how you do it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when will you be online again sir?
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