Date: Sep 20, 2017 11:45 PM
Author: Dan Christensen
Subject: Re: 0 = 1

On Wednesday, September 20, 2017 at 10:46:20 PM UTC-4, Dan Christensen wrote:
> On Wednesday, September 20, 2017 at 9:40:18 PM UTC-4, conway wrote:
> > > On Wednesday, September 6, 2017 at 3:01:29 PM UTC-4,
> > > conway wrote:

> > > > 0 and 1 share identical spaces. ( 1 + (-1) )
> > > proves this....if 0 did not have a space on the
> > > number line the equation would equal -1. 0 and 1 do
> > > NOT share a value in common. 0 is NOT equal to 1.
> > >
> > > Thanks for confirming that, contrary your heading, we
> > > still have 0=/=1.
> > >
> > >

> > > > according to value. But according to space they
> > > ARE equivalent.
> > > >
> > >
> > > Huh??? Not sure what kind of wonky equivalence
> > > relation you have in mind, but it sure isn't
> > > equality. 0 and 1 are NOT generally interchangeable.
> > >
> > > So, we still have 0x=0 and 0x=/=1 for all x in R. And
> > > 0=/=1. Whew!
> > >
> > >
> > > Dan
> > >
> > > Download my DC Proof 2.0 software at
> > > http://www.dcproof.com
> > > Visit my Math Blog at
> > > http://www.dcproof.wordpress.com
> > >
> > >
> > >
> > >

> >
> > Dan
> >
> >
> > To be fair to you....ok....I was not "precise" in my title. I chose it to add "flare".......HOWEVER.....zero and 1 are interchangeable with "space"......but not with value.....
> >
> > consider..."abstractly"...
> >
> >
> > If I have an empty box... that is zero. If I fill the empty box with 1 of anything....that is 1. 1 still has the same "box" that zero had....its just that it is "filled"...

>
> You really need to formalize this system of yours. By this, I mean you need to define everything using purely in the language of predicate logic and maybe set theory. Any inferences you draw should be based not on any spatial intuition as here, but purely on the formal rules of logic as applied to these definition/axioms. You can insert some prose comments about "empty boxes" etc. to help the reader visualize what you are talking about, but they are not to be used in making any logical inferences.
>


This is not merely personal preference, pickiness or pedantry. It really is the "acid test" of your ideas and how they work together. If they cannot be formalized in a way similar to what I have described here, they aren't really mathematics.


>
> Dan
>
> Download my DC Proof 2.0 software at http://www.dcproof.com <--- CHECK IT OUT!
>
> Visit my Math Blog at http://www.dcproof.wordpress.com