Definitions (1 Viewer)

[Constip8edSkunk]

What does it mean when a function is described as a)injective and b)subjective?

 

[McLake]

Injective = one-to-one corrospondance.
So, for every y value there is a corresponding (and unique) x value. Note, this dosn't mean that all x values have a y value.

Subjective = onto.
For every y value in the domain there is an x value.

 

[Affinity]

and bijective means both

 

[Grey Council]

whats a function then? I thought it was when every x value has only one y value. Or is it when every y value has one x value? :-S

*hides his head in shame*

 

[turtle_2468]

A function is when every x value only has ONE y value.
eg if you take the "dodgy" unrestricted version of inverse sin,
arcsin(1/2)=pi/6
but arcsin(1/2)=13pi/6 as well
so having 2 y values like that is not allowed, because it means you can have more than 1 possible "answer" to the same thing, and thus that those two are the same (clearly silly)...

A function has to satisfy "vertical line test"
To be injective (equivalent to having an inverse function) it has to satisfy the "horizontal line test"
surjective is when it takes all values in the codomain... but that'll be covered in uni

 

[Constip8edSkunk]

ok i think i understand...

correct me if im wrong, one can set the codomain of a function right? and the surjectivity is based on the codomain set? so that f(x)=x^2, f:R->R would not be surjective but if f: R->R+ then it would be?

 

[Affinity]

yea.. just a minor point, f:r->r+ is not well defined because f(0) is not in the codomain

 

[Grey Council]

hehe, i was right then, originally. Before Mclake (yeah you McLake. And don't you take out he mod stick ) confused me with injective and subjective definitions.

 

[McLake]

Originally posted by Grey Council
hehe, i was right then, originally. Before Mclake (yeah you McLake. And don't you take out he mod stick ) confused me with injective and subjective definitions.

I'm sorry *runs off in shame*