Today I came across some great math works at a local bookstore, I don't recall all the titles I browse through. I saw one book mentioned about a proof of 1+1=2 in a book called "Principia Mathematica" by Russell and Whitehead.
See this entry in wiki for details.
Waita minute, I thought Principia was the great Newton work? (I saw a handwritten copy of that at a museum! Um, I dare to complain, excuse me, Issac Newton Sir, can you please write a bit more legibly please) But this is not Newton's work of course. Even if I can see what Newton wrote I still can't understand, because it is in Latin. Even if it is in English I can't understand because it is some tough reading(!)
Check that scan out in the middle of that wiki entry of the Whitehead and Russell's work. An unintelligentable looking proof (ok, to me) showing... "From this proposition it will follow, when addition has been defined, that 1+1=2". I have no idea what those asterisks and stuff are, perhaps refering to some other section of this thing.
I can't validate this proof, but isn't it strange trying to prove 1+1=2?
Toddlers know 1+1=2. You don't need such proof.
Look, numbers are NAMES for quantities. You teach a toddler like this: See that ball over there? Bring it to me... Good boy. You have one ball. Can you repeat? One ball.
Look, can you find another ball? Bring it to me... Good! You start with 1 ball, now you give me another one, we say you have TWO balls.
1+1 means you start with 1, add another one, how many do you have now?
1+1=2 by definition, you don't need such unintelligentable proof.
3 comments:
I guess there are too many things we don't need, yet they are produced by entrepreneurs or so-called scholars... their argument would be "how do you know something is not needed?" An example is number theory applied to cryptography.
No one should be fascinated or write about about 1 + 1 = 2.
A smart 3 year old knows 1+1 is 2, and there is really nothing more to it.
Let me add that 1+1=10 base 2 is not clever, nor funny.
While it is true that 99.999% of the world can gets by life without ever knowing that there is a need to prove 1+1=2, it isn't true that it was a useless exercise.
In Russell and Whitehead's case, they wanted to ensure that every mathematical result was grounded in some irrefutable basic truth (i.e. axioms). 1+1=2 happens to be based on much simpler results, even though it appears to be as simple as it gets.
I will liken them to cosmologists, theoretical physicists, exploring the boundaries of our understanding, to ensure that we truly know what we know.
Galileo's laws of motion was something we 'know', but in actual fact it is merely an approximation (a very good one) of reality.
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