November 15, 2016 Tuesday
Bedtime Story
Basic Notation of Modern Set Theory
Basic Notation of Modern Set Theory
Let me enlist the basic notation of modern set theory.
The letter N represents set of natural numbers.
Natural numbers are positive integers 1, 2, 3…that are used for
counting and ordering.
The topic of ordering is itself a fascinating topic which I might
deal later if I remember to.
The letter Q represents set of rational numbers.
A rational numbers is any number that can be expressed as a p/q
where both p and q are integers.
Moreover, the q cannot be zero.
In terms of decimal expansion, a rational number is such that it
either always terminates after a finite number of digits or repeats same finite
series of digits over and over again.
Example: 8/3 or 2.666666666666…
The letter R represents the set of real numbers.
Real numbers are a fascinating bunch of guys.
There is no formal or rigorous definition of the real numbers.
This may not bother people like you and I, but it becomes a source
of great disconcertion for pure mathematicians.
A real number is thought of as any point on an infinitely long
number line or sometimes also known as real line.
It includes both the natural numbers, the rational numbers and
even the irrational number such as √2 and transcendental numbers such as pi or π.
An irrational number is that which cannot be expressed as a
fraction and when written in decimal form its digits neither do they terminate
nor repeat indefinitely.
So for example √2 cannot be expressed in any fraction such as 1/2
or 3/2 or 1/3 and when put in the decimal form goes on endlessly
1.41421356237309504…with no known pattern.
Transcendental are a rare breed of numbers, with the finest and
well known examples being pi or π and the Euler’s number e.
Its rigorous definition was given by the great Euler.
A transcendental number is defined as a real or a complex number
that is not a root of a non-zero polynomial equation with integer coefficients.
Try to sleep over this definition of transcendental number.
It will give you sleepless nights.
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:
Symbol R represents the set of all real numbers
This slide may be bit premature as it describes the set theory pictorially that i have yet to discuss
This will give you a rough idea on how many real numbers can fit in even in a span of tiny real number line
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