So Dan Christensen has still problems with Euclids even
and odd natural numbers. He is still bat shit carzy
and high as a kite. Woa!

Yes Dan Christensen ultra moron you got it, almost:

Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 00:35:26 UTC+2:
> So, everything that is isn't a natural number is both
not even and not odd. How wonky is that?
https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/ASEgcINuAQAJ

Just spell it out correctly, or are you linguistically impaired?

everything that is isn't a natural number is both
not an even natural number and not an odd natural number .

Gerald Edgar schrieb am Donnerstag, 6. Januar 1994 um 20:26:21 UTC+1:
> Mathematical Cranks
> This is the title of an interesting book by Underwood Dudley, 1992.
> There is an (also interesting) review of it by Ian Stewart in the
> January issue of the American Mathematical Monthly.
> --
> Gerald A. Edgar Internet: ed...@math.ohio-state.edu
> Department of Mathematics Bitnet: EDGAR@OHSTPY
> The Ohio State University telephone: 614-292-0395 (Office)
> Columbus, OH 43210 -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

The blistering imbecil Dan Christensen never read this here:

6. An even number is that which is divisible into two equal parts.
7. An odd number is that which is not divisible into two equal parts,
or that which differs by a unit from an even number.
http://aleph0.clarku.edu/~djoyce/elements/bookVII/defVII6.html

What does it say? It doesn't say "even" and "odd". It says
"even number" and "odd number".

The syphilitic idiot Dan Christensen is linguistically impaired.

Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 00:52:56 UTC+2:
> So Dan Christensen has still problems with Euclids even
> and odd natural numbers. He is still bat shit carzy
> and high as a kite. Woa!
>
> Yes Dan Christensen ultra moron you got it, almost:
>
> Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 00:35:26 UTC+2:
> > So, everything that is isn't a natural number is both
> not even and not odd. How wonky is that?
> https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/ASEgcINuAQAJ
>
> Just spell it out correctly, or are you linguistically impaired?
>
> everything that is isn't a natural number is both
> not an even natural number and not an odd natural number .
> Gerald Edgar schrieb am Donnerstag, 6. Januar 1994 um 20:26:21 UTC+1:
> > Mathematical Cranks
> > This is the title of an interesting book by Underwood Dudley, 1992.
> > There is an (also interesting) review of it by Ian Stewart in the
> > January issue of the American Mathematical Monthly.
> > --
> > Gerald A. Edgar Internet: ed...@math.ohio-state.edu
> > Department of Mathematics Bitnet: EDGAR@OHSTPY
> > The Ohio State University telephone: 614-292-0395 (Office)
> > Columbus, OH 43210 -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

Or to make it crystal clear for the megatron jerk which
goes by the name Dan Christensen, these two formulas:

ALL(a):[ ~a e n => ~Even(a) ]
ALL(a):[ ~a e n => ~Odd(a) ]

Don't say:

Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 00:35:26 UTC+2:
"So, everything that isn't a natural number is both
not even and not odd. How wonky is that? "
http://aleph0.clarku.edu/~djoyce/elements/bookVII/defVII6.html

They say:

"everything that isn't a natural number is both
not an even natural number and not an odd natural number . "

Why? Because I use and prove them from Euclids
definition, which does not define "even" and "odd",
it only defines "even number" and "odd number",

which is done as follows:

ALL(a):[Even(a) <=> a e n & EXIST(b):[b e n & a=b+b]]
ALL(a):[Odd(a) <=> a e n & ~EXIST(b):[b e n & a=b+b]]

Nothing wonky since it refers to Euclid. The only
wonky thing is Dan Christensens syphilistic brain.

Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 01:17:18 UTC+2:
> The blistering imbecil Dan Christensen never read this here:
>
> 6. An even number is that which is divisible into two equal parts.
> 7. An odd number is that which is not divisible into two equal parts,
> or that which differs by a unit from an even number.
> http://aleph0.clarku.edu/~djoyce/elements/bookVII/defVII6.html
>
> What does it say? It doesn't say "even" and "odd". It says
> "even number" and "odd number".
>
> The syphilitic idiot Dan Christensen is linguistically impaired.
> Mostowski Collapse schrieb am Donnerstag, 12. Mai 2022 um 00:52:56 UTC+2:
> > So Dan Christensen has still problems with Euclids even
> > and odd natural numbers. He is still bat shit carzy
> > and high as a kite. Woa!
> >
> > Yes Dan Christensen ultra moron you got it, almost:
> >
> > Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 00:35:26 UTC+2:
> > > So, everything that is isn't a natural number is both
> > not even and not odd. How wonky is that?
> > https://groups.google.com/g/sci.logic/c/gV50jEU6fvQ/m/ASEgcINuAQAJ
> >
> > Just spell it out correctly, or are you linguistically impaired?
> >
> > everything that is isn't a natural number is both
> > not an even natural number and not an odd natural number .
> > Gerald Edgar schrieb am Donnerstag, 6. Januar 1994 um 20:26:21 UTC+1:
> > > Mathematical Cranks
> > > This is the title of an interesting book by Underwood Dudley, 1992.
> > > There is an (also interesting) review of it by Ian Stewart in the
> > > January issue of the American Mathematical Monthly.
> > > --
> > > Gerald A. Edgar Internet: ed...@math.ohio-state.edu
> > > Department of Mathematics Bitnet: EDGAR@OHSTPY
> > > The Ohio State University telephone: 614-292-0395 (Office)
> > > Columbus, OH 43210 -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

On Wednesday, May 11, 2022 at 7:30:11 PM UTC-4, Mostowski Collapse wrote:
> Or to make it crystal clear for the megatron jerk which
> goes by the name Dan Christensen, these two formulas:
>
> ALL(a):[ ~a e n => ~Even(a) ]
> ALL(a):[ ~a e n => ~Odd(a) ]
>

Poor Jan Burse. If only he could be made to understand that:

1. For all natural numbers x, we say that x is even iff there exists natural number y such that x=2*y.

2. We say that x is odd iff x is not even.

Simple. Easy to understand (for most people anyway). And no wonky results to explain away.

Don't hold your breath, folks.

[snip]

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

What makes you think 1. and 2. are the
definitions I was talking about?

Dan Christensen schrieb:
> On Wednesday, May 11, 2022 at 7:30:11 PM UTC-4, Mostowski Collapse wrote:
>> Or to make it crystal clear for the megatron jerk which
>> goes by the name Dan Christensen, these two formulas:
>>
>> ALL(a):[ ~a e n => ~Even(a) ]
>> ALL(a):[ ~a e n => ~Odd(a) ]
>>
>
> Poor Jan Burse. If only he could be made to understand that:
>
> 1. For all natural numbers x, we say that x is even iff there exists natural number y such that x=2*y.
>
> 2. We say that x is odd iff x is not even.
>
> Simple. Easy to understand (for most people anyway). And no wonky results to explain away.
>
> Don't hold your breath, folks.
>
> [snip]
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>

When you are an ultra moron as you are you, that cannot
keep track of context, you should not use the same predicate
name in different contexts as you do here:

Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 04:08:02 UTC+2:
> > CASE 1
> > ALL(a):[a in n => [Even(a) <=> EXIST(b):[b in n & a=2*b]]]
> > CASE 2
> > ALL(a):[Even(a) <=> a in n & EXIST(b):[b in n & a=2*b]]

Better introduce two different predicate names, like here:

CASE 1
ALL(a):[a in n => [Evenness(a) <=> EXIST(b):[b in n & a=2*b]]]
CASE 2
ALL(a):[Evennumber(a) <=> a in n & EXIST(b):[b in n & a=2*b]]

Mostowski Collapse schrieb:
>
> What makes you think 1. and 2. are the
> definitions I was talking about?
>
> Dan Christensen schrieb:
>> On Wednesday, May 11, 2022 at 7:30:11 PM UTC-4, Mostowski Collapse wrote:
>>> Or to make it crystal clear for the megatron jerk which
>>> goes by the name Dan Christensen, these two formulas:
>>>
>>> ALL(a):[ ~a e n => ~Even(a) ]
>>> ALL(a):[ ~a e n => ~Odd(a) ]
>>>
>>
>> Poor Jan Burse. If only he could be made to understand that:
>>
>> 1. For all natural numbers x, we say that x is even iff there exists
>> natural number y such that  x=2*y.
>>
>> 2. We say that x is odd iff x is not even.
>>
>> Simple. Easy to understand (for most people anyway). And no wonky
>> results to explain away.
>>
>> Don't hold your breath, folks.
>>
>> [snip]
>>
>> Dan
>>
>> Download my DC Proof 2.0 freeware at http://www.dcproof.com
>> Visit my Math Blog at http://www.dcproof.wordpress.com
>>
>

Some Litmus Formulas are these.
This here is not provable:

|/- ALL(a):[~a e n => ~Evenness(a)]
|/- ALL(a):[~a e n => ~Oddness(a)]
|/- ALL(a):[a e n <=> Evenness(a) v Oddness(a)]
|/- ALL(a):[Oddness(a) <=> a e n & ~Evenness(a)]

On the other hand this is provable:

|- ALL(a):[~a e n => ~Evennumber(a)]
|- ALL(a):[~a e n => ~Oddnumber(a)]
|- ALL(a):[a e n <=> Evennumber(a) v Oddnumber(a)]
|- ALL(a):[Oddnumber(a) <=> a e n & ~Evennumber(a)]

https://en.wikipedia.org/wiki/Litmus

Mostowski Collapse schrieb:
> When you are an ultra moron as you are you, that cannot
> keep track of context, you should not use the same predicate
> name in different contexts as you do here:
>
> Dan Christensen schrieb am Donnerstag, 12. Mai 2022 um 04:08:02 UTC+2:
> > > CASE 1
> > > ALL(a):[a in n => [Even(a) <=> EXIST(b):[b in n & a=2*b]]]
> > > CASE 2
> > > ALL(a):[Even(a) <=> a in n & EXIST(b):[b in n & a=2*b]]
>
> Better introduce two different predicate names, like here:
>
> CASE 1
> ALL(a):[a in n => [Evenness(a) <=> EXIST(b):[b in n & a=2*b]]]
> CASE 2
> ALL(a):[Evennumber(a) <=> a in n & EXIST(b):[b in n & a=2*b]]
>
> Mostowski Collapse schrieb:
>>
>> What makes you think 1. and 2. are the
>> definitions I was talking about?
>>
>> Dan Christensen schrieb:
>>> On Wednesday, May 11, 2022 at 7:30:11 PM UTC-4, Mostowski Collapse
>>> wrote:
>>>> Or to make it crystal clear for the megatron jerk which
>>>> goes by the name Dan Christensen, these two formulas:
>>>>
>>>> ALL(a):[ ~a e n => ~Even(a) ]
>>>> ALL(a):[ ~a e n => ~Odd(a) ]
>>>>
>>>
>>> Poor Jan Burse. If only he could be made to understand that:
>>>
>>> 1. For all natural numbers x, we say that x is even iff there exists
>>> natural number y such that  x=2*y.
>>>
>>> 2. We say that x is odd iff x is not even.
>>>
>>> Simple. Easy to understand (for most people anyway). And no wonky
>>> results to explain away.
>>>
>>> Don't hold your breath, folks.
>>>
>>> [snip]
>>>
>>> Dan
>>>
>>> Download my DC Proof 2.0 freeware at http://www.dcproof.com
>>> Visit my Math Blog at http://www.dcproof.wordpress.com
>>>
>>
>