December 07, 2016 Wednesday
Bedtime Story
Introduction to Predicate and Power Set
3. Axiom of Separation
also known as the axiom schema of
specification:
This is considered to be a very important axiom as it restricts
the comprehension of sets.
It also introduces the concept of predicate.
In mathematical logic a predicate is a statement that can be true
or false depending on the values its variables will produce.
Mathematically, it can be seen as a Boolean valued function such
that predicate P: x
{true, false}
The axiom schema of separation can be stated as follows:
Given a set A, there is a set B such that given any set x, x is a
member of set B if and only if x is a member of set A and predicate
holds for x.
This can be further simplified.
Given a set A and a predicate P, we can find a subset B of A whose
members are exactly the members of A that satisfies P.
To make it even pithier, the axiom can be stated thus:
Every subclass of a set that is defined by a predicate is itself a
set.
4. Axiom of power set:
This axiom deals with the notion of power set symbolized with the
letter Weierstrass p
also called pe.
The power set of a set S is denoted by
(S).
The power set is defined by the axiom of power set which states
that:
Given any set x there is a set
(x) such that, given any set z, z is a member of
(x) if and only if every element of z is also an element of x.
In other words, for every set x there is a set
(x) consisting precisely of the subsets of x.
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