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Member Posts: 3941 From: Duluth, Minnesota, U.S. (West end of Lake Superior) Joined: Member Rating: 10.0 |
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Author | Topic: 1+1=2 | |||||||||||||||||||||
Minnemooseus Member Posts: 3941 From: Duluth, Minnesota, U.S. (West end of Lake Superior) Joined: Member Rating: 10.0 |
From Joz at Fact Theory Falacy #39:
quote: 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]
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joz Inactive Member |
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 naturalnumbers 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]
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joz Inactive Member |
Does this mean i get to head the new math dept at Whatsamatter U?
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Minnemooseus Member Posts: 3941 From: Duluth, Minnesota, U.S. (West end of Lake Superior) Joined: Member Rating: 10.0 |
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
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joz Inactive Member |
quote: 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]
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Peter Member (Idle past 1479 days) Posts: 2161 From: Cambridgeshire, UK. Joined: |
quote: Not entirely sure here, but I think 1 + 1 = 2 is empirically based like the above in A level math too though.
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joz Inactive Member |
quote: 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.....
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Minnemooseus Member Posts: 3941 From: Duluth, Minnesota, U.S. (West end of Lake Superior) Joined: Member Rating: 10.0 |
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.
------------------BS degree, geology, '83 Professor, geology, Whatsamatta U Old Earth evolution - Yes Godly creation - Maybe
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joz Inactive Member |
quote: A little limerick I came across.... On Liquor Productionby David M. Smith A friend who's in liquor productionOwns a still of astounding construction. The alcohol boils Through old magnet coils; She says that it's "proof by induction."
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compmage Member (Idle past 5153 days) Posts: 601 From: South Africa Joined: |
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...
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Brad McFall Member (Idle past 5033 days) Posts: 3428 From: Ithaca,NY, USA Joined: |
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)??
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NeilUnreal Inactive Member |
From about 10 messages back:
quote: 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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