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Codomain question

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Jack

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Apr 21, 2013, 9:42:27 AM4/21/13
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Hi again,
Is it valid to speak of a 'range' of a codomain? If not, what would be
the proper term?
With thanks.


Frederick Williams

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Apr 21, 2013, 12:08:56 PM4/21/13
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If f: X -> Y is a function, then Y is its codomain. The range of _f_
is
{y | f(x) = y for some x in X}. So the range is a subset of the
codomain. What do you mean when you write of the range of a codomain?

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

Jack

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Apr 21, 2013, 8:19:11 PM4/21/13
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"Frederick Williams" <freddyw...@btinternet.com> wrote in message
news:51740F18...@btinternet.com...
> Jack wrote:
>>
>> Hi again,
>> Is it valid to speak of a 'range' of a codomain? If not, what would be
>> the proper term?
>> With thanks.
>
> If f: X -> Y is a function, then Y is its codomain. The range of _f_
> is
> {y | f(x) = y for some x in X}. So the range is a subset of the
> codomain. What do you mean when you write of the range of a codomain?
>

Looks like I have got it wrong then. If I say that f yields a continuous set
of values the lowest of which is -oo and the highest of which is oo, then
what verb describes what f does with respect to the reals?



William Elliot

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Apr 21, 2013, 9:47:47 PM4/21/13
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On Mon, 22 Apr 2013, Jack wrote:
> "Frederick Williams" <freddyw...@btinternet.com> wrote in message

> >> Hi again,
> >> Is it valid to speak of a 'range' of a codomain? If not, what would be
> >> the proper term?
> >
> > If f: X -> Y is a function, then Y is its codomain. The range of _f_
> > is
> > {y | f(x) = y for some x in X}. So the range is a subset of the
> > codomain. What do you mean when you write of the range of a codomain?

> Looks like I have got it wrong then. If I say that f yields a continuous
> set of values the lowest of which is -oo and the highest of which is oo,
> then what verb describes what f does with respect to the reals?

That is nonsense as -oo and oo aren't real numbers numbers

A correct statement would be: f yields a continuous set of
values the lowest of which is a and the highest of which is b

That is not always possible. For example f(x) = e^x
never yields it's lowest value, nor does f yield a
highest value. In fact, f is unbounded above.

> then what verb describes what f does with respect to the reals?

Ranging over the reals.

Jack

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Apr 22, 2013, 8:09:38 AM4/22/13
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>
>> then what verb describes what f does with respect to the reals?
>
> Ranging over the reals.
>

I thought that, to say it ranges over the reals would describe its domain. I
want to describe its codomain.


Jack

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Apr 22, 2013, 5:47:06 PM4/22/13
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"Frederick Williams" <freddyw...@btinternet.com> wrote in message
news:51740F18...@btinternet.com...
> Jack wrote:
>>
>> Hi again,
>> Is it valid to speak of a 'range' of a codomain? If not, what would be
>> the proper term?
>> With thanks.
>
> If f: X -> Y is a function, then Y is its codomain. The range of _f_
> is
> {y | f(x) = y for some x in X}. So the range is a subset of the
> codomain.

Oh I think I understand now. Thanks,


Frederick Williams

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Apr 28, 2013, 5:32:40 AM4/28/13
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Its image is the reals, or it is onto the reals, or it is a surjection.
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