Saturday, January 24, 2009

1=2

There are several "proofs" that result in the absurd claim that 1=2.  Here's one from Bill:

      Step 1: Let a=b.

      Step 2: Then a2 = ab,

      Step 3: a2 + a2 = a2 + ab,

      Step 4: 2a2 = a2 + ab,

      Step 5: 2a2 – 2ab = a2 + ab – 2ab,

      Step 6: and 2a2 – 2ab = a2 - ab.

      Step 7: This can be written as, 2(a2 – ab) = 1(a2 – ab)

Step 8: and canceling the  (a2 – ab) from both sides gives 1=2.


But to actually claim that you KNOW that 1 does NOT equal 2 you would need to have reasons.  So, what is the reason, i.e. what is the fallacious step in this proof?  Click on the step you take to be fallacious.  If you are incorrect, perhaps you don't have good grounds for thinking 1=1. 

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4 comments:

  1. Bill RosserJanuary 27, 2009 at 8:26 AM

    This is a tricky one, I'm glad you posted it

    ReplyDelete
  2. Bill RosserJanuary 29, 2009 at 8:15 AM

    There is a problem with calling God a being so great none could be greater, that leads to the false presumption that we know that God can't be greater, who's to say that an almighty being isn't so mighty that he could very well improve himself and make him self almightier (not a word but you know what I mean) To say that God can't raise the upper limit of greatness and perfection would imho deminish God's greatness and imply that we really understand what God's greatness is. It's like suggesting that God is the end of a line rather than a ray going towards infinity. If we mere mortals are capable of evolving from our humble beginnings in huts chucking spears at animals, who's to say God can't do anything we can do only 10 times better

    January 29, 2009 8:12 AM

    ReplyDelete
  3. Brian GlenneyJanuary 30, 2009 at 5:30 AM

    I like the "ray going towards infinity" analogy to God's greatness.

    So, the idea is that the God of the Jews was not as great, say, as the God of the Christians as he got greater with the manifestation of Jesus and the Holy Spirit on Earth.

    Nice. Here are a few ways to respond, none of which seems entirely satisfactory to me:

    1. I guess that this is where one has to get dogmatic, and deny that God's greatness is dependent on a process.

    2. Rework the "greatness" claim to temporal indexicals. So rather than "God is the greatest possible" one must claim, "God is the greatest possible at every time."

    Thanks Bill

    ReplyDelete
  4. AnonymousMarch 5, 2009 at 7:42 AM

    In step 8 you divide both sides by (a^2 - ab) which is zero and not a valid operation for precisely this reason.

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