Linear transformations

[DeadOriginal]

Say I have a linear transformation T:V$\rightarrow$W. Can I necessarily say that T(V)$\subseteq$W?

I feel like T being a linear transformation would make the function behave enough to force things to not be undefined but I can't be certain..

 

[verty]

Of course. T(V) is the range which is always a subset of the codomain.

 

[DeadOriginal]

Hmm. I see. Thanks! I'm losing my mind.

 

[verty]

Do you understand that this is true for any function ever? That is how functions are defined, the range is a subset of the codomain.

 

[DeadOriginal]

Yea. I messed up my reasoning with the range and the domain. I switched them around thinking that if something was undefined then it wouldn't be in the range. Like if x=0 and f(x)=1/x then 1/0 is not in the range but it is x=0 that is not in the domain.

 

[A David]

Do you understand that this is true for any function ever? That is how functions are defined, the range is a subset of the codomain.

Any mapping ever, really.

 

[verty]

Any mapping ever, really.

I still have the old mindset where every collection is a set and every mapping is a function. Probably this is from reading books not much more recent than the 60's.