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

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Dan Christensen

Posts: 2,619
Registered: 7/9/08
Re: Peano's rot in action for you!
Posted: Mar 5, 2014 1:44 PM
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On Wednesday, March 5, 2014 1:25:03 PM UTC-5, John Gabriel wrote:
> So,
>
> 0 = {}
>
> 1 = { {} } = {0}
>
> 2 = { {}, {{}} } = {0, 1}
>
>


This is not from Peano who would have: 1=S(0), 2=S(1), etc.


>
> We know 1 - 0 = 1
>


We can construct the addition function on N using Peano. Addition is closed on N. Subtraction is not, so we would have define the '-' operator as follows:

For all x, y, z in N we have: x-y=z if and only if x = z+y.

Apply to the above: 1 - 0 = 1 iff 1 = 1 + 0

>
>
> But using Peano's crap:
>
>
>
> { {} } - {} = {}
>


Not from Peano.

> 1 - 0 = 0
>


Wrong because 1 =/= 0+0. Back to the drawing board, John Gabriel.

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
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Date Subject Author
2/25/14
Read Infinity: The Story So Far
Dan Christensen
2/25/14
Read Re: Infinity: The Story So Far
Brian Q. Hutchings
2/25/14
Read Re: Infinity: The Story So Far
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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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