Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.

https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)

Dan

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

Dan Christensen wrote:

> Most presentations of the axioms of group theory seem to give both right
> and left identities and inverses, which turns out to be somewhat
> redundant. Here, given the axioms for group (g,*) with only right
> identity and inverses, we formally prove that the right identity and
> inverses are also a left identity and inverse respectively.

you took the "vaccines" and are not yet dead?? You stupid immigrant of
cacanada. What is your real name? You real name!! You khazar goys just
change your names and move to cacanada, a shithole back in a garden.

On Wednesday, July 5, 2023 at 3:13:14 PM UTC-4, Rocky Karahalios wrote:
> Dan Christensen wrote:
>
> > Most presentations of the axioms of group theory seem to give both right
> > and left identities and inverses, which turns out to be somewhat
> > redundant. Here, given the axioms for group (g,*) with only right
> > identity and inverses, we formally prove that the right identity and
> > inverses are also a left identity and inverse respectively.
> you took the "vaccines" and are not yet dead?? You stupid immigrant of
> cacanada. What is your real name? You real name!! You khazar goys just
> change your names and move to cacanada, a shithole back in a garden.

Hey, Nazi Boy! Enjoying the crowded cemeteries full of young Russian boys who died for nothing in your genocidal war of conquest in Ukraine? You had better go into hiding if you don't want to be conscripted and end up like them.

Correction: Should be "only RIGHT identity and inverses"

On Wednesday, July 5, 2023 at 3:07:53 PM UTC-4, Dan Christensen wrote:
> Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.
>
> https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Dan Christensen wrote:

>> you took the "vaccines" and are not yet dead?? You stupid immigrant of
>> cacanada. What is your real name? You real name!! You khazar goys just
>> change your names and move to cacanada, a shithole back in a garden.
>
> Hey, Nazi Boy! Enjoying the crowded cemeteries full of young Russian
> boys who died for nothing in your genocidal war of conquest in Ukraine?
> You had

you are going to pay for it, you stinking nazi modrefucker. You can't hide
in cacanada, which is a shithole.

*_Ukraine_Update_July_3,4,_2023_*
https://b%69%74%63hute.com/video/5rDmALckjDc0

The khazar gypsy goy zelenske is planning to
strike power plant with dirty bomb, *_this_night_* in zaporozja!!

*_Nuclear_Energy_Advisor_Says_zelenske_Strikes_ZNPP_*
https://b%69%74%63hute.com/video/u3B9ji0xCRko

Come on Dan Christensen. Do you really want to tell me:

- You CANNOT show that U is redundant in Trichotomy,
representable by T and F?

- But you CAN show that left identity is redundant in
a group, representable by right identity?

You sure that this is your story? Sounds like a bad joke.

Dan Christensen schrieb am Mittwoch, 5. Juli 2023 um 21:07:53 UTC+2:
> Most presentations of the axioms of group theory seem to give
both right and left identities and inverses, which turns out to be
somewhat redundant. Here, given the axioms for group (g,*) with
only right identity and inverses, we formally prove that the right
identity and inverses are also a left identity and inverse respectively.
>
> https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, July 5, 2023 at 10:07:53 PM UTC+3, Dan Christensen wrote:
> Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.
>
> https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Why people are attacking you constantly Dan C?

Doesn't that suggest something to you where you don't think of? No wonder!

But certainly you are suffering constantly from something in mind 🙃! Sure

BKK

Why don't you show a proof BKK, make yourself useful
once in your life. So far you didn't post anything interesting.

bassam karzeddin schrieb am Donnerstag, 14. September 2023 um 20:32:33 UTC+2:
> On Wednesday, July 5, 2023 at 10:07:53 PM UTC+3, Dan Christensen wrote:
> > Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.
> >
> > https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com
> Why people are attacking you constantly Dan C?
>
> Doesn't that suggest something to you where you don't think of? No wonder!
>
> But certainly you are suffering constantly from something in mind 🙃! Sure
>
> BKK

On Thursday, September 14, 2023 at 9:39:51 PM UTC+3, Mild Shock wrote:
> Why don't you show a proof BKK, make yourself useful
> once in your life. So far you didn't post anything interesting.
> bassam karzeddin schrieb am Donnerstag, 14. September 2023 um 20:32:33 UTC+2:
> > On Wednesday, July 5, 2023 at 10:07:53 PM UTC+3, Dan Christensen wrote:
> > > Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.
> > >
> > > https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
> > >
> > > Dan
> > >
> > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > Visit my Math Blog at http://www.dcproof.wordpress.com
> > Why people are attacking you constantly Dan C?
> >
> > Doesn't that suggest something to you where you don't think of? No wonder!
> >
> > But certainly you are suffering constantly from something in mind 🙃! Sure
> >
> > BKK

Why can't you Mild Shock version well-understand my too simple proofs instead?

I do believe that I have proven ALL my unique & so peculiar & rarest historical claims with too simple elementary & numerical "irrefutable" proofs FOR SURE

But so unfortunately, since only my unique vision & proofs are against the academic mainstreams dogmatic beliefs & their achievements, then certainly it would be globally denied & fought to death as well

Go learn my proofs & rewrite them in a logical mathematical way you are pretending!

Bassam karzeddin

On Thursday, September 14, 2023 at 2:26:41 PM UTC-4, Mild Shock wrote:
> Come on Dan Christensen. Do you really want to tell me:
>
> - You CANNOT show that U is redundant in Trichotomy,
> representable by T and F?
>
[snip]

Apparently, you cannot tell a trichotomy from a dichotomy. See my posting just now in the thread "The Liar Paradox: My latest blog posting" at sci.logic.

Dan

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

The proof is as easy as follows:
- We don't need to use predicates
- We don't need to use sets
- We can show it with propositional variables

All we need to prove is:
Equivalence: (((¬T ∧ ¬F) ↔ U)
Trichotomy II: ¬(T∧F)
Trichotomy I: ((T ∨ (F∨U)) ∧ (¬(T∧F) ∧ (¬(T∧U) ∧ ¬(F∧U))))
Equivalence & Trichotomy II <=> Trichotomy I

Here is a proof:
(((¬T ∧ ¬F) ↔ U) ∧ ¬(T∧F)) ↔ ((T ∨ (F∨U)) ∧ (¬(T∧F) ∧ (¬(T∧U) ∧ ¬(F∧U)))) is valid.
https://www.umsu.de/trees/#(~3T~1~3F~4U)~1~3(T~1F)~4(T~2F~2U)~1~3(T~1F)~1~3(T~1U)~1~3(F~1U)

Easy, wasn't it?

Dan Christensen schrieb am Donnerstag, 14. September 2023 um 22:14:31 UTC+2:
> On Thursday, September 14, 2023 at 2:26:41 PM UTC-4, Mild Shock wrote:
> > Come on Dan Christensen. Do you really want to tell me:
> >
> > - You CANNOT show that U is redundant in Trichotomy,
> > representable by T and F?
> >
> [snip]
>
> Apparently, you cannot tell a trichotomy from a dichotomy. See my posting just now in the thread "The Liar Paradox: My latest blog posting" at sci.logic.
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Or instead of using Wolfgang Schwarz tree tool, you
can also look at truth tables, and see that it is the same:

Equivalence & Trichotomy II
Fs Ts Us (((¬Ts ∧ ¬Fs) ↔ Us) ∧ ¬(Ts ∧ Fs))
F F T T
F T F T
T F F T
https://web.stanford.edu/class/cs103/tools/truth-table-tool/

Trichotomy I
Fs Ts Us ((Ts ∨ (Fs ∨ Us)) ∧ (¬(Ts ∧ Fs) ∧ (¬(Ts ∧ Us) ∧ ¬(Fs ∧ Us))))
F F T T
F T F T
T F F T
https://web.stanford.edu/class/cs103/tools/truth-table-tool/

Q.E.D.

Mild Shock schrieb am Donnerstag, 14. September 2023 um 22:26:03 UTC+2:
> The proof is as easy as follows:
> - We don't need to use predicates
> - We don't need to use sets
> - We can show it with propositional variables
>
> All we need to prove is:
> Equivalence: (((¬T ∧ ¬F) ↔ U)
> Trichotomy II: ¬(T∧F)
> Trichotomy I: ((T ∨ (F∨U)) ∧ (¬(T∧F) ∧ (¬(T∧U) ∧ ¬(F∧U))))
> Equivalence & Trichotomy II <=> Trichotomy I
>
> Here is a proof:
> (((¬T ∧ ¬F) ↔ U) ∧ ¬(T∧F)) ↔ ((T ∨ (F∨U)) ∧ (¬(T∧F) ∧ (¬(T∧U) ∧ ¬(F∧U)))) is valid.
> https://www.umsu.de/trees/#(~3T~1~3F~4U)~1~3(T~1F)~4(T~2F~2U)~1~3(T~1F)~1~3(T~1U)~1~3(F~1U)
>
> Easy, wasn't it?
> Dan Christensen schrieb am Donnerstag, 14. September 2023 um 22:14:31 UTC+2:
> > On Thursday, September 14, 2023 at 2:26:41 PM UTC-4, Mild Shock wrote:
> > > Come on Dan Christensen. Do you really want to tell me:
> > >
> > > - You CANNOT show that U is redundant in Trichotomy,
> > > representable by T and F?
> > >
> > [snip]
> >
> > Apparently, you cannot tell a trichotomy from a dichotomy. See my posting just now in the thread "The Liar Paradox: My latest blog posting" at sci..logic.
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

In case you disagree with this equality, can
you name one truth table row, where:

(((¬Ts ∧ ¬Fs) ↔ Us) ∧ ¬(Ts ∧ Fs))

and this here:

((Ts ∨ (Fs ∨ Us)) ∧ (¬(Ts ∧ Fs) ∧ (¬(Ts ∧ Us) ∧ ¬(Fs ∧ Us))))

differ? If you can name a row, I will believe you.

Mild Shock schrieb am Donnerstag, 14. September 2023 um 22:26:52 UTC+2:
> Or instead of using Wolfgang Schwarz tree tool, you
> can also look at truth tables, and see that it is the same:
>
> Equivalence & Trichotomy II
> Fs Ts Us (((¬Ts ∧ ¬Fs) ↔ Us) ∧ ¬(Ts ∧ Fs))
> F F T T
> F T F T
> T F F T
> https://web.stanford.edu/class/cs103/tools/truth-table-tool/
>
> Trichotomy I
> Fs Ts Us ((Ts ∨ (Fs ∨ Us)) ∧ (¬(Ts ∧ Fs) ∧ (¬(Ts ∧ Us) ∧ ¬(Fs ∧ Us))))
> F F T T
> F T F T
> T F F T
> https://web.stanford.edu/class/cs103/tools/truth-table-tool/
>
> Q.E.D.
> Mild Shock schrieb am Donnerstag, 14. September 2023 um 22:26:03 UTC+2:
> > The proof is as easy as follows:
> > - We don't need to use predicates
> > - We don't need to use sets
> > - We can show it with propositional variables
> >
> > All we need to prove is:
> > Equivalence: (((¬T ∧ ¬F) ↔ U)
> > Trichotomy II: ¬(T∧F)
> > Trichotomy I: ((T ∨ (F∨U)) ∧ (¬(T∧F) ∧ (¬(T∧U) ∧ ¬(F∧U))))
> > Equivalence & Trichotomy II <=> Trichotomy I
> >
> > Here is a proof:
> > (((¬T ∧ ¬F) ↔ U) ∧ ¬(T∧F)) ↔ ((T ∨ (F∨U)) ∧ (¬(T∧F) ∧ (¬(T∧U) ∧ ¬(F∧U)))) is valid.
> > https://www.umsu.de/trees/#(~3T~1~3F~4U)~1~3(T~1F)~4(T~2F~2U)~1~3(T~1F)~1~3(T~1U)~1~3(F~1U)
> >
> > Easy, wasn't it?
> > Dan Christensen schrieb am Donnerstag, 14. September 2023 um 22:14:31 UTC+2:
> > > On Thursday, September 14, 2023 at 2:26:41 PM UTC-4, Mild Shock wrote:
> > > > Come on Dan Christensen. Do you really want to tell me:
> > > >
> > > > - You CANNOT show that U is redundant in Trichotomy,
> > > > representable by T and F?
> > > >
> > > [snip]
> > >
> > > Apparently, you cannot tell a trichotomy from a dichotomy. See my posting just now in the thread "The Liar Paradox: My latest blog posting" at sci.logic.
> > > Dan
> > >
> > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > Visit my Math Blog at http://www.dcproof.wordpress.com

onsdag 5 juli 2023 kl. 21:07:53 UTC+2 skrev Dan Christensen:
> Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.
>
> https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
https://proofwiki.org/wiki/Left_Inverse_for_All_is_Right_Inverse

On Thursday, September 14, 2023 at 4:26:03 PM UTC-4, Mild Shock wrote:
> The proof is as easy as follows:

[snip]

See my thread on this topic in the thread, "The Liar Paradox: My latest blog posting"

Dan

On Thursday, September 14, 2023 at 10:17:52 PM UTC+3, bassam karzeddin wrote:
> On Thursday, September 14, 2023 at 9:39:51 PM UTC+3, Mild Shock wrote:
> > Why don't you show a proof BKK, make yourself useful
> > once in your life. So far you didn't post anything interesting.
> > bassam karzeddin schrieb am Donnerstag, 14. September 2023 um 20:32:33 UTC+2:
> > > On Wednesday, July 5, 2023 at 10:07:53 PM UTC+3, Dan Christensen wrote:
> > > > Most presentations of the axioms of group theory seem to give both right and left identities and inverses, which turns out to be somewhat redundant. Here, given the axioms for group (g,*) with only right identity and inverses, we formally prove that the right identity and inverses are also a left identity and inverse respectively.
> > > >
> > > > https://dcproof.com/GroupLeftRightIdentityInverses.htm (only 123 lines)
> > > >
> > > > Dan
> > > >
> > > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > > Visit my Math Blog at http://www.dcproof.wordpress.com
> > > Why people are attacking you constantly Dan C?
> > >
> > > Doesn't that suggest something to you where you don't think of? No wonder!
> > >
> > > But certainly you are suffering constantly from something in mind 🙃! Sure
> > >
> > > BKK
> Why can't you Mild Shock version well-understand my too simple proofs instead?
>
> I do believe that I have proven ALL my unique & so peculiar & rarest historical claims with too simple elementary & numerical "irrefutable" proofs FOR SURE
>
> But so unfortunately, since only my unique vision & proofs are against the academic mainstreams dogmatic beliefs & their achievements, then certainly it would be globally denied & fought to death as well
>
> Go learn my proofs & rewrite them in a logical mathematical way you are pretending!
>
>
> Bassam karzeddin