November 28, 2016 Monday
Bedtime Story
Dedekind Provided the Proof for the First Theorem
The most common example that is cited is the division of the
number line with the root of 2, the most famous irrational number that cannot
be expressed as a ratio of two integers or fraction.
In this case, the number that lies exactly to the left hand side
of √2 will be another new irrational number.
In words of Dedekind himself:
“Whenever, then, we have to do with a cut produced by no rational
number, we create a new irrational number, which we regard as completely
defined by this cut…
From now on, therefore, to every definite cut there corresponds a
definite rational or irrational number…”
Dedekind himself was dealing with number theory and these kinds of
ideas related to set, so that he was possibly the first and the only
mathematician (besides Cantor’s former teachers Karl Weierstrass and Leopold
Kronecker) who could not only understand Cantor work but even contribute to it
through correspondence.
His greatest contribution was to provide the proof to Cantor’s
first theorem that defined the set of real algebraic numbers to be countable.
Dedekind did something which the likes of us can never imagine.
He saw a connection between algebraic numbers and polynomials.
He then defined the height of polynomials and then ordered the
real roots of the same height by the numeric order.
This orderings put the real algebraic number into a sequence.
Quite understandably, this is a difficult idea for us
non-mathematicians to grasp.
Cantor was very thankful to Dedekind for his help which he wrote
to him in private, but left it out in the paper for which Dedekind never
forgave him and even stopped his correspondence for years.
So in that way, even mathematicians are just like other human apes.
They too seek acclaim, acknowledgement and whatever glory
mathematics is capable of giving from their own peer group.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night and my fellow cousin ape.
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, may I
suggest this large collection of Kids Songs:
No comments:
Post a Comment