October 19, 2017 Thursday
Bedtime Story
Example of Recursion Function is Factorial
The famous Entscheidungsproblem goes
something like this:
Suppose you are given a statement of
first-order logic in a system of finite axioms.
In this case, does there exists an
algorithm (series of logical finite number of steps) than can answer “yes” or
“No” to the question “Is that statement universally valid?”
This means to say that the statement is valid
in every structure satisfying the axioms.
Now it seems to me (as I do not know for
sure) that recursion might be a very useful tool in problem solving as it has
almost a magical way of implementing itself using something known as stacking.
Now I am letting myself run away and
letting the cart come before the horse.
So let me rewind my thoughts a little bit
and start from beginning.
Most of us have a vague notion of the idea
of recursion as something that keeps repeating.
That is generally correct though
mathematicians would not be happy with just that kind of vague definition.
They need to define everything very
formally and precisely.
By the way, recursion is one of those
concepts just like the mathematical constant
(base of natural logarithm, approximately
equal to 2.71828 and limit of (1 +
)n
as n approaches infinity) that keeps surfacing almost everywhere.
Before I define recursion, let me give you
a mathematical example of recursion.
A very simple mathematical function that
can be dealt recursively is the factorial function.
Now we all know the concept of mathematical
factorial.
Factorial of any non-negative integer n is
written down as n!
The value of factorial n is obtained by
multiplying all the positive integers less than n and n itself.
So factorial 6 or 6! = 6 x 5 x 4 x 3 x 2 x
1
Now there is another way of defining
factorial of a number.
A factorial of a non-negative integer n is
the product of n and factorial n-1
So n! = n x n-1!
So 6! = 6 x 5!
Now if you would ask how to define
factorial 5, you already know the answer.
5! = 5 x 4!
This will go on till be reach one as
factorial 1 or 1!= 1
So we have a dead end in a manner of
speaking and that allows us to arrive at a solution.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
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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