December 08, 2016 Thursday
Bedtime Story
Power Set and the Axiom of the Union
The concept of power set is not difficult and becomes lucid with
an example.
Consider a set x that consist of {2, 4, 6} 3 smallest positive
even integers.
The subsets of x would be:
{} or Ø an empty or null set
{2}
{4}
{6}
{2, 4}
{2, 6}
{4, 6}
{2, 4, 6}
Thus the power set of x would be:
{{}, {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6}}
5. Axiom of the Union:
Given any set A, there is a set B such that, for any element c, c
is a member of B if and only if there is a set D such that c is a member of D
and D is a member of A.
In simpler words, for every set A, there corresponds a set
A, the union of A that consists of elements precisely as the
elements of A.
In essence, the union of a set is a set.
In the next bedtime story, I will try to take you through the
sixth axiom which is the axiom of choice and one of the founding axioms of
mathematics and set theory.
It was essentially construed to tackle the idea of a set
containing infinite subsets and then defining a function that would enable
“picking” out an element from each subset (which physically is impossible
considering the infinity).
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:
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