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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..

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- Thread starter DeadOriginal
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In summary, the conversation discusses the relationship between a linear transformation T:V##\rightarrow##W and the possibility of T(V) being a subset of W. The participants also touch upon the concept of range and codomain, clarifying that the range is always a subset of the codomain for any function. They also mention the difference between undefined and not being in the domain, and the fact that this is true for all mappings. The conversation ends with one participant mentioning their old mindset relating to collections and mappings.

- #1

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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..

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- #2

Homework Helper

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

- #3

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

- #4

Homework Helper

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- #5

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- #6

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verty said:

Any mapping ever, really.

- #7

Homework Helper

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A David said: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.

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