Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Topic: prove no largest prime
Replies: 51   Last Post: Jul 12, 2012 3:15 AM

 Messages: [ Previous | Next ]
 Frederick Williams Posts: 2,166 Registered: 10/4/10
Re: prove no largest prime
Posted: Jul 5, 2012 8:31 AM

quasi wrote:
>
> quasi wrote:

> >quasi wrote:
> >>
> >>To prove something doesn't exist, unless there's an axiom

> >(or prior theorem)
> >>that asserts such nonexistence, you pretty much have to
> >>start by assuming it _does_ exist, and then try to derive

> >
> >But in the absence of a nonexistence axiom, if it's based on
> >a prior theorem that asserts nonexistence, then at some lower
> >level, it's _based_ on a proof by contradiction.

>
> I think I claimed way too much.
>
> After all, if we accept DeMorgan's laws, then to prove
>
> "There does not exist x such that P(x)"
>
> one can simply prove the equivalent form
>
> "For all x, not P(x)"
>
> which does not have the form of a proof by contradiction.

It depends. One way of proving "For all x, not P(x)" is to assume P(a),
where a is any individual of the required type and nothing that follows
depends on which particular thing a is, deduce a contradiction from that
assumption, conclude not-P(a). But a was not special, so for all x,
not-P(x).

--
The animated figures stand
Adorning every public street
And seem to breathe in stone, or
Move their marble feet.

Date Subject Author
7/4/12 Tim923
7/4/12 FredJeffries@gmail.com
7/4/12 gnasher729
7/4/12 quasi
7/4/12 quasi
7/4/12 quasi
7/4/12 quasi
7/5/12 Frederick Williams
7/7/12 Peter Webb
7/8/12 |-| E R C
7/8/12 Graham Cooper
7/8/12 Barry Schwarz
7/8/12 Graham Cooper
7/8/12 Graham Cooper
7/8/12 Frederick Williams
7/8/12 Pubkeybreaker
7/8/12 Graham Cooper
7/8/12 Graham Cooper
7/9/12 David Bernier
7/9/12 Frederick Williams
7/11/12 Graham Cooper
7/11/12 Frederick Williams
7/11/12 Graham Cooper
7/11/12 Frederick Williams
7/11/12 Graham Cooper
7/11/12 Frederick Williams
7/11/12 Graham Cooper
7/11/12 Pubkeybreaker
7/11/12 Frederick Williams
7/11/12 Gary G Forbis
7/11/12 Graham Cooper
7/11/12 dilettante
7/11/12 Gary G Forbis
7/12/12 dilettante
7/12/12 Gary G Forbis
7/11/12 Graham Cooper
7/11/12 Graham Cooper
7/11/12 Usher73
7/8/12 Peter Webb
7/11/12 Frederick Williams
7/9/12 Peter Webb
7/9/12 Graham Cooper
7/9/12 Graham Cooper
7/5/12 Frederick Williams
7/5/12 quasi
7/4/12 Bart Goddard
7/5/12 trj
7/4/12 Ken.Pledger@vuw.ac.nz
7/4/12 gnasher729
7/5/12 Tim923
7/5/12 Graham Cooper
7/5/12 Frederick Williams