Proof that 1+1=2

[Anastasia13]

[url="http://mathforum.org/library/drmath/view/51551.html"]http://mathforum.org/library/drmath/view/51551.html[/url]

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.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.

Edited September 4, 2005 by Light and Truth

[RC_]

[Tony]

my brrain hurts

[ReinnieR]

[quote name='Light and Truth' date='Sep 4 2005, 12:34 AM'][url="http://mathforum.org/library/drmath/view/51551.html"]http://mathforum.org/library/drmath/view/51551.html[/url]

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.

Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
  Def: Let a and b be in N. If b = 0, then define a + b = a.
      If b isn't 0, then let c' = b, with c in N, and define
      a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
      1 + 1 = (1 + 0)'
      Now use the first part of the definition of + on the sum in
      parentheses:  1 + 1 = (1)' = 1' = 2  Q.E.D.
[right][snapback]710394[/snapback][/right]
[/quote]


ok so how would explain the trinity to anti-trinitarians will you use the same formula

when 1+1+1=1

how are we to explain this??

[phatcatholic]

wow.................................humans are notorious for making things MUCH more complicated than they need to be........

[FlyLikeABird]

[voiciblanche]

Pssh. If Sally has one apple, and Billy has one apple, then together they have two apples... is enough proof for me.

[FlyLikeABird]

Proof that 2+1=4

"Where two or three are gathered in my name, there am I in their midst"

:

[let_go_let_God]

Ohhh boy, is it sad that I understand that and I haven't even started my math classes yet and I haven't done basic proofs since I took pre-algebra as an 8th grader.....

I need to get a life outside possible school work....

God bless-
LGLG

[Thy Geekdom Come]

[quote name='ReinnieR' date='Sep 4 2005, 02:11 AM']ok so how would explain the trinity to anti-trinitarians will you use the same formula

when 1+1+1=1

how are we to explain this??
[right][snapback]710419[/snapback][/right]
[/quote]

1+1+1=1 is not a proper definition of the Trinity. There is one divine nature in Three Persons. One divine nature, not one divine nature for each of them. There is only one, and yet, each of the Three Persons possesses it fully and completely (because it is freely given amongst them, and thus, belongs to all Three), but they do not share it. The Divine Persons, existing wholly within one another (because of their love, They each give themselves over entirely to the other, and thus Jesus says, "I am in the Father and the Father is in Me"), each hold the Divine Nature entirely because they hold each Other entirely. Therefore, the equation given implies that each Person has a separate and distinct Divine Nature, but since the Divine Nature is pure essence, I don't believe there can be more than one...it's just a single undivided (pure essence can't be divided, or else you would have two of the same thing, and you can't have two of the exact same thing, because then neither of them would be individual things, and in order for them to be divided, they would each need to be individual), unmultiplied (can't multiply infinity) essence. So really, it's more like 1 (wholly and entirely possessed by each of 3, but not divided among them, nor multiplied for them)=1

When you get to the Divine Persons, of course, it's simpler... 1+1+1=3



If I've made any error in this, please let a CS correct me.

[prose]

It's funny you posted that. I was just wondering about how to prove that equation....

[Proud2BCatholic139]

I wish I was better in math.

[ardillacid]

I do too

[Iacobus]

Wait till they get tricky and try to divide by zero. Those sly foxes.

[curtins]

I cant beleive someone would waste there time trying to scientifcally prove 1+1=2 it just amazes me. What are people going to think up next? sceientifically prove that the grass is green?

[theculturewarrior]

You haven't read [i]1984![/i]

[dspen2005]

[Snarf]

I think it was Bertrand Russel that wrote a 250+ page definition of the number 1. If I'm ever stoned again, maybe I'll read it.

[son_of_angels]

I would read Descartes if I were you. Then you could see that it is a distinct possibility that 1+1 does not equal two, because some evil genius makes me miscount every time, and, since, we count through the use of our senses, which only amount to ideas inflicted on us, then we cannot conclude that there is any two things at all.

[Snarf]

Yeah, I've read the Meditations on Philosophy. One of my friends is a philosophy major who hates epistemology, on grounds that it's "tautological". I should make her a cd with NIN's "Right Where It Belongs".