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Topic: Why don't texts give a stronger version of Zorn's lemma?
Replies: 9   Last Post: Nov 22, 2013 6:12 AM

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Paul

Posts: 385
Registered: 7/12/10
Re: Why don't texts give a stronger version of Zorn's lemma?
Posted: Nov 22, 2013 4:56 AM
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On Friday, November 22, 2013 12:09:01 AM UTC, Peter Percival wrote:
> Paul wrote:
>

> > On Wednesday, November 20, 2013 5:06:35 PM UTC, Peter Percival
>
> > wrote:
>
> >> James Waldby wrote:
>
> >>
>
> >>> On Wed, 20 Nov 2013 12:28:17 +0000, Peter Percival wrote:
>
> >>
>
> >>>> William Elliot wrote:
>
> >>
>
> >>>>> How can it be stronger? They're both equivalent.
>
> >>
>
> >>>>
>
> >>
>
> >>>> I know even less about English than I know about maths, but it
>
> >>>> seems to
>
> >>
>
> >>>> me that
>
> >>
>
> >>>
>
> >>
>
> >>>> They're both equivalent.
>
> >>
>
> >>>
>
> >>
>
> >>>> is ungrammatical. I think it should be
>
> >>
>
> >>>
>
> >>
>
> >>>> They're equivalent to each other.
>
> >>
>
> >>>
>
> >>
>
> >>>> or
>
> >>
>
> >>>
>
> >>
>
> >>>> They're both equivalent to <some third thing>.
>
> >>
>
> >>>
>
> >>
>
> >>> No, "They're both equivalent" isn't ungrammatical. Some may see
>
> >>> it as
>
> >>
>
> >>> slightly awkward or pleonastic but I think most native speakers
>
> >>> will,
>
> >>
>
> >>> without remark, take it as meaning "They're equivalent" (which is
>
> >>> what I'd
>
> >>
>
> >>> have written if it were so). In appropriate context, "They're
>
> >>> equivalent"
>
> >>
>
> >>> has the same meaning but is less verbose than "They're equivalent
>
> >>> to each
>
> >>
>
> >>> other".
>
> >>
>
> >>
>
> >>
>
> >> I'm happy with 'they're equivalent'; it's 'they're *both*
>
> >> equivalent'
>
> >>
>
> >> that reads oddly to me. (But I may be mad.)
>
> >>
>
> >>
>
> > You're totally correct that it reads oddly. This is because of the
>
> > pleonasm, as has been pointed out.
>
> >
>
> > However, the problem in the phrasing is not of a _grammatical_
>
> > nature, so there is no grammatical error. From the point of view of
>
> > grammar, it wouldn't be wrong to say "they're both green" rather than
>
> > "they're both equivalent."
>
>
>
> A thing on its own may be green. A thing on its own cannot be
>
> equivalent, it can only be equivalent to another thing (or itself; since
>
> this is sci.math we must allow that "is equivalent to" is an equivalence
>
> relation).
>
>

...

I was trying to explain why I think you are not identifying a _grammatical_ error. I didn't say that you didn't identify an error. Remember that you used the word "ungrammatical".

From a grammatical perspective, "They're both equivalent." is correct because "equivalent" is an adjective and the sentence therefore has the correct grammatical structure.
You're addressing semantics, which is different.

Likewise, it is grammatically correct to say "The dead cat sprinted at a speed of seventy miles per hour."

It's grammatically correct but it contradicts science.

Paul Epstein




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