Re: Review of Mueckenheims book.

On Mar 5, 8:33 pm, David Marcus <DavidMar...@xxxxxxxxxxxxxx> wrote:

The normal definition of "function" includes specifying the domain and
codomain. So, a given function only has one codomain.

Not in set theory; not with the definition of 'codomain' that was
given:

c is a codomain of f <-> range(f) subset_of c.

So for NO set is there a UNIQUE codomain.

For every set, there is a unique range, but not a unique codomain,
since there are lots and lots of sets that are supersets of any range.

If you want to have a different defintion of 'codomain' so that there
is a unique codomain for each function, then fine, but with the
definition that has been given in this thread, it is a theorem that
every set has more than one codomain.

MoeBlee




.

Relevant Pages

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  • Re: Review of Mueckenheims book.
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