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Topic: Infinity: The Story So Far
Replies: 298   Last Post: Apr 7, 2014 7:30 AM

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thenewcalculus@gmail.com

Posts: 1,616
Registered: 11/1/13
Re: Peano's rot in action for you!
Posted: Mar 5, 2014 11:16 PM
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On Wednesday, 5 March 2014 21:00:48 UTC+2, Peter Percival wrote:
> John Gabriel wrote:
>

> > So,
>
> > 0 = {}
>
> > 1 = { {} } = {0}
>
> > 2 = { {}, {{}} } = {0, 1}
>
>
>
> That is not Peano, it is von Neumann.
>
>
>

> > We know 1 - 0 = 1
>
>
>
> Yes, but if 1 and 0 are defined to be particular sets, then - has to be
>
> defined to be an operator on sets. Or, more precisely, - is the inverse
>
> of + and + has to be defined to be an operator on sets. So this...
>

> >
>
> > But using Peano's crap:
>
> >
>
> > { {} } - {} = {}
>
> > 1 - 0 = 0
>
>
>
> ... doesn't work because you are assuming A - B means "the set A with
>
> the element B removed". And if one were to define subtraction of von
>
> Neumann natural numbers (and symbolize it with a minus sign) then one
>
> wouldn't define it that way.
>

> >
>
> > Interesting, we can't even subtract using Peano's rot.
>
>
>
> There is some truth in that. Peano's axioms are about these creatures:
>
> 0,1,2,3,.. and generally subtraction is not defined on them. Consider 3
>
> - 5, etc.
>
>
>

> > We can try defining the set objects as:
>
> >
>
> > 0 = { }
>
> > 1 = { {} } = { 0 }
>
> > 2 = { { { } } } = { 1 }
>
>
>
> Still not Peano, Zermelo.
>
>
>

> > Now, 2 - 0 = 2
>
> >
>
> > But using Peano:
>
> >
>
> > { {{ }} } - {} = { {} }
>
>
>
> You have changed from your original meaning of - applied to sets, though
>
> to what I am not sure.
>
>
>

> > 2 - 0 = 1
>
> >
>
> > Interesting, and moron academics are actually teaching this rot in university lecture rooms.
>
>
>
> At this time of year in the Northern temperate zone out of doors would
>
> be impractical.
>
>
>

> > Can you believe it? These are Peano's "sound axioms"! :-) What a joke!
>
>
>
> Actually, I'm not sure how your first use of - is defined, but since
>
> it's irrelevant to defining
>
>
>
> the inverse of + on the natural numbers defined
>
> à la von Neumann or Zermelo
>
>
>
> it doesn't matter much.
>
>
>
> -- ...


Von Neumann got it from Peano. It is very much FROM PEANO! :-)


Date Subject Author
2/25/14
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Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
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2/27/14
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thenewcalculus@gmail.com
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thenewcalculus@gmail.com
2/27/14
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Dan Christensen
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thenewcalculus@gmail.com
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thenewcalculus@gmail.com
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Dan Christensen
2/28/14
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Dan Christensen
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2/28/14
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thenewcalculus@gmail.com
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thenewcalculus@gmail.com
3/2/14
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Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/2/14
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3/2/14
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Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/2/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/2/14
Read Re: Infinity: The Story So Far
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3/3/14
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3/3/14
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3/2/14
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3/2/14
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thenewcalculus@gmail.com
3/2/14
Read Re: How I established my axioms.
Jürgen R.
3/2/14
Read Re: How I established my axioms.
thenewcalculus@gmail.com
3/3/14
Read Re: How I established my axioms.
New Balance
3/2/14
Read Re: How I established my axioms.
Wizard-Of-Oz
3/2/14
Read Re: How I established my axioms.
New Balance
3/4/14
Read Infinity does not exist and Peano was a moron.
thenewcalculus@gmail.com
3/4/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/4/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/4/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/4/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/4/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/4/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/5/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/5/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/5/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/4/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
3/5/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
3/5/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/5/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
3/5/14
Read Re: Infinity: The Story So Far
Brian Q. Hutchings
3/5/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/5/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/5/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/5/14
Read No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/5/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/5/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/5/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/6/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/6/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/6/14
Read Re: No need for spaghetti "axioms".
Dan Christensen
3/6/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/5/14
Read Re: No need for spaghetti "axioms".
YBM
3/6/14
Read Re: No need for spaghetti "axioms".
New Balance
3/6/14
Read Re: No need for spaghetti "axioms".
thenewcalculus@gmail.com
3/6/14
Read poster boy for "let's die-a-log
Brian Q. Hutchings
3/5/14
Read Peano's rot in action for you!
thenewcalculus@gmail.com
3/5/14
Read Re: Peano's rot in action for you!
Dan Christensen
3/5/14
Read Re: Peano's rot in action for you!
thenewcalculus@gmail.com
3/5/14
Read Re: Peano's rot in action for you!
Dan Christensen
3/5/14
Read Re: Peano's rot in action for you!
Peter Percival
3/5/14
Read Re: Peano's rot in action for you!
thenewcalculus@gmail.com
3/5/14
Read Re: Peano's rot in action for you!
Martin Shobe
3/5/14
Read Re: Peano's rot in action for you!
Wizard-Of-Oz
3/5/14
Read Re: Peano's rot in action for you!
Wizard-Of-Oz
3/5/14
Read Re: Peano's rot in action for you!
Wizard-Of-Oz
3/5/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/6/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/12/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com

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