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Author Topic:   1+1=2
Minnemooseus
Member
Posts: 3941
From: Duluth, Minnesota, U.S. (West end of Lake Superior)
Joined: 11-11-2001
Member Rating: 10.0


Message 1 of 13 (3759)
02-07-2002 9:48 PM


From Joz at Fact Theory Falacy #39:
quote:
Actualy i gave you a series of steps to follow in order to prove 1+1=2 (yes Moose it can be done!) they are as follows:
Step 1) Define 1.
Step 2) define addition.
Step 3) define 2.
Step 4)combine steps 1 through 3.
I would like to pursue this more. It seems to me that you are defining 1+1 as being equal to 2, rather than proving 1+1=2.
Does the definition of step 2 and/or step 3 incorporate the definition of step 1?
Moose
------------------
BS degree, geology, '83
Professor, geology, Whatsamatta U
Old Earth evolution - Yes
Godly creation - Maybe
[This message has been edited by minnemooseus, 02-07-2002]

Replies to this message:
 Message 2 by joz, posted 02-07-2002 9:54 PM Minnemooseus has replied
 Message 4 by joz, posted 02-07-2002 9:59 PM Minnemooseus has not replied
 Message 12 by Brad McFall, posted 04-28-2002 5:37 PM Minnemooseus has not replied

  
joz
Inactive Member


Message 2 of 13 (3762)
02-07-2002 9:54 PM
Reply to: Message 1 by Minnemooseus
02-07-2002 9:48 PM


Ok i was going to save this but here goes mathematical proof that 1+1=2....
The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:
P1.1 is in N.
P2.If x is in N, then its "successor" x' is in N.
P3.There is no x such that x' = 1.
P4.If x isn't 1, then there is a y in N such that y' = x.
P5.If S is a subset of N, 1 is in S, and the implication (x in S => x' in S) holds, then S = N.
Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1,
then define a + b = a' (using P1 and P2).
If b isn't 1, then let c' = b, with c in N (using P4),
and define a + b = (a + c)'.
Then you have to define 2:
Def: 2 = 1'
2 is in N by P1, P2, and the definition of 2.
Theorem: 1 + 1 = 2
Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.
[This message has been edited by joz, 02-07-2002]

This message is a reply to:
 Message 1 by Minnemooseus, posted 02-07-2002 9:48 PM Minnemooseus has replied

Replies to this message:
 Message 5 by Minnemooseus, posted 02-08-2002 8:31 PM joz has replied

  
joz
Inactive Member


Message 4 of 13 (3764)
02-07-2002 9:59 PM
Reply to: Message 1 by Minnemooseus
02-07-2002 9:48 PM


Does this mean i get to head the new math dept at Whatsamatter U?

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 Message 1 by Minnemooseus, posted 02-07-2002 9:48 PM Minnemooseus has not replied

  
Minnemooseus
Member
Posts: 3941
From: Duluth, Minnesota, U.S. (West end of Lake Superior)
Joined: 11-11-2001
Member Rating: 10.0


Message 5 of 13 (3891)
02-08-2002 8:31 PM
Reply to: Message 2 by joz
02-07-2002 9:54 PM


Joz, I've been looking at you proof some, and I have some requests:
1)In plain language, can you define what a "natural number" is? I presume it means "positive integer". 0 and negative integers are excluded.
2)As used in postulate 2 - can you define "successor"?
Moose
------------------
BS degree, geology, '83
Professor, geology, Whatsamatta U
Old Earth evolution - Yes
Godly creation - Maybe

This message is a reply to:
 Message 2 by joz, posted 02-07-2002 9:54 PM joz has replied

Replies to this message:
 Message 6 by joz, posted 02-08-2002 11:07 PM Minnemooseus has not replied

  
joz
Inactive Member


Message 6 of 13 (3898)
02-08-2002 11:07 PM
Reply to: Message 5 by Minnemooseus
02-08-2002 8:31 PM


quote:
Originally posted by minnemooseus:
Joz, I've been looking at you proof some, and I have some requests:
1)In plain language, can you define what a "natural number" is? I presume it means "positive integer". 0 and negative integers are excluded.
2)As used in postulate 2 - can you define "successor"?
Moose

I wish I could lay claim to it but I had it from my maths teacher at A level, what he said led me to believe that it was the generaly accepted proof....
1)Yep positive non zero integer... A natural no. is a number you could use to count say sheep in a flock. i.e. not a negative, fraction, irrational or imaginary number (it would be an intresting flock of sheep that consisted of a complex number of sheep)(zero is precluded as if you had a flock with no sheep in it you wouldn`t have a flock)....
Also note in the flock of sheep analogy the maximum size of the possible flock extends towards infinity.... No "well you can only take care of x number of sheep" rules apply....
2)First natural No. is one its succsessor is the next positive non zero integer....
[This message has been edited by joz, 02-08-2002]
[This message has been edited by joz, 02-08-2002]

This message is a reply to:
 Message 5 by Minnemooseus, posted 02-08-2002 8:31 PM Minnemooseus has not replied

Replies to this message:
 Message 7 by Peter, posted 02-11-2002 10:02 AM joz has replied

  
Peter
Member (Idle past 1479 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 7 of 13 (4130)
02-11-2002 10:02 AM
Reply to: Message 6 by joz
02-08-2002 11:07 PM


quote:
Originally posted by joz:
I wish I could lay claim to it but I had it from my maths teacher at A level, what he said led me to believe that it was the generaly accepted proof....
1)Yep positive non zero integer... A natural no. is a number you could use to count say sheep in a flock. i.e. not a negative, fraction, irrational or imaginary number (it would be an intresting flock of sheep that consisted of a complex number of sheep)(zero is precluded as if you had a flock with no sheep in it you wouldn`t have a flock)....
Also note in the flock of sheep analogy the maximum size of the possible flock extends towards infinity.... No "well you can only take care of x number of sheep" rules apply....
2)First natural No. is one its succsessor is the next positive non zero integer....
[This message has been edited by joz, 02-08-2002]
[This message has been edited by joz, 02-08-2002]

Not entirely sure here, but I think
1 + 1 = 2
is empirically based
... I have seen it proved something
like the above in A level math too though.

This message is a reply to:
 Message 6 by joz, posted 02-08-2002 11:07 PM joz has replied

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 Message 8 by joz, posted 02-12-2002 2:25 PM Peter has not replied

  
joz
Inactive Member


Message 8 of 13 (4256)
02-12-2002 2:25 PM
Reply to: Message 7 by Peter
02-11-2002 10:02 AM


quote:
Originally posted by Peter:
Not entirely sure here, but I think
1 + 1 = 2
is empirically based
... I have seen it proved something
like the above in A level math too though.

I`m pretty sure that 1+1=2 is a direct result of the properties of the set of natural numbers and the addition operator rather than being purely empirical....
Admitedly 1+1=2 was accepted as fact for a long time based purely on empirical observation but can be proved as above....
My point in raising the proof of 1+1=2 was to show KP that he was insisting that a repeated empirical observation (1+1=2) was a fact while also insisting that another repeated empirical observation (evolution) was not.....
My point was that KP could not *prove* 1+1=2 in the same fashion that he requires evolution to be proved and yet accepted 1+1=2 as a fact based on a string of empirical observations the sort of reasoning that he and other creationists are critical of in terms of evolution.....

This message is a reply to:
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Replies to this message:
 Message 9 by Minnemooseus, posted 02-13-2002 12:08 AM joz has replied

  
Minnemooseus
Member
Posts: 3941
From: Duluth, Minnesota, U.S. (West end of Lake Superior)
Joined: 11-11-2001
Member Rating: 10.0


Message 9 of 13 (4345)
02-13-2002 12:08 AM
Reply to: Message 8 by joz
02-12-2002 2:25 PM


This all reminds me of my first college math class. Doing (what I recall) was called proofs by induction. You started out with something that was obviously true, went through some wierd process, ended up where you started, and it was considered proven.
Moose
------------------
BS degree, geology, '83
Professor, geology, Whatsamatta U
Old Earth evolution - Yes
Godly creation - Maybe

This message is a reply to:
 Message 8 by joz, posted 02-12-2002 2:25 PM joz has replied

Replies to this message:
 Message 10 by joz, posted 02-14-2002 9:44 AM Minnemooseus has not replied

  
joz
Inactive Member


Message 10 of 13 (4494)
02-14-2002 9:44 AM
Reply to: Message 9 by Minnemooseus
02-13-2002 12:08 AM


quote:
Originally posted by minnemooseus:
This all reminds me of my first college math class. Doing (what I recall) was called proofs by induction. You started out with something that was obviously true, went through some wierd process, ended up where you started, and it was considered proven.
Moose

A little limerick I came across....
On Liquor Production
by David M. Smith
A friend who's in liquor production
Owns a still of astounding construction.
The alcohol boils
Through old magnet coils;
She says that it's "proof by induction."

This message is a reply to:
 Message 9 by Minnemooseus, posted 02-13-2002 12:08 AM Minnemooseus has not replied

Replies to this message:
 Message 11 by compmage, posted 04-09-2002 10:36 AM joz has not replied

  
compmage
Member (Idle past 5153 days)
Posts: 601
From: South Africa
Joined: 08-04-2005


Message 11 of 13 (8378)
04-09-2002 10:36 AM
Reply to: Message 10 by joz
02-14-2002 9:44 AM


This proving of 1+1=2 reminds me of something. I am not sure if I read it somewhere or heard it. I am also not sure if it was ment as a joke or not.
It goes something like this...
2+2=5, for exceptionally large values of 2.
------------------
I have conquered worlds...

This message is a reply to:
 Message 10 by joz, posted 02-14-2002 9:44 AM joz has not replied

  
Brad McFall
Member (Idle past 5033 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 12 of 13 (9081)
04-28-2002 5:37 PM
Reply to: Message 1 by Minnemooseus
02-07-2002 9:48 PM


Min, being aware of algebraic use in Mendelism can you or anyone inform me why B. Russel felt that Kant had lost it's relevance to the chain of being on the existence of Frege's arithmetic. Every time I solve for this sign I end up with Stebbins notion of an open-habitat (for plants)??

This message is a reply to:
 Message 1 by Minnemooseus, posted 02-07-2002 9:48 PM Minnemooseus has not replied

  
NeilUnreal
Inactive Member


Message 13 of 13 (9655)
05-15-2002 1:08 AM


From about 10 messages back:
quote:
P3.There is no x such that x' = 1.
Woa! Blast from the past. I was instantly transported back to the classroom where my sentential calculus professor explained the reason for including this proposition in the proof. It was an old building with high ceilings and wood floors...
-Neil

  
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