January 13, 2017 Friday
Bedtime Story
The Other Principia:
Peano then presented to the world his axiomatization of natural
numbers and arithmetic in a book form in the year of 1889 at a tender age of
31.
The book is called:
The Principles of Arithmetic by a New Method.
In Latin (the language in which it was originally published), it
is called:
Arithmetices
principia, nova methodo exposita.
Just as a reminder, this is yet another landmark book that went by
the name of Principia.
This book, besides containing Peano’s axiomatization of natural
numbers had revolutionary contributions in the field of mathematical logic and
set theory which as stated earlier, was in its infancy.
Before I list out the Peano axioms, let me tell you broadly how
they are divided.
The nine axioms are stated out via three type of statements.
The first axiom and the statement is assertive and simply
postulates the existence of at least one member of the set of natural numbers.
This is exactly in the manner of Euclid who began geometry with a
set of postulates that he and later the world at large would consider to be
“self-evident”.
The second type of statements (of which there are four) are about
equality.
These are statements of underlying logic which any average grasp
would incline to accept without resorting to far-fetched imagination.
The third type of statements are first-order and second-order
statements.
The first-order statements are three that exhibit the fundamental
properties of successor operation which John von Neumann had used later.
The second-order statement is just one and it states the principle
of mathematical induction that operates on the natural numbers.
What are these first-order and second-order statements?
Do they not make you curious?
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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