December 13, 2016 Tuesday
Bedtime Story
Axiom of Choice: How Ridicuolusly Non-Mathematical It Sounds
By a rough estimate, every year more than 250,000 theorems are
proved (from hypotheses and conjectures).
6. Axiom of choice:
Axiom of choice is just another such self-evident truth that even
you will agree is too obviously self-evident and there is nothing to fuss about.
All that the axiom of choice states is this:
Given a set of non-empty boxes, it is possible to choose an object
from each box.
This is it.
Ridiculous, don’t you think so?
It does not even sound mathematics.
And average ape like me could have said it, isn’t it?
What is so special about it?
What has it to do anything with the continuum hypothesis?
Let us study it a bit more closely.
This axiom takes into consideration many disjoint sets.
Say a collection of 10 boxes each containing at least 1 item.
Meaning, there won’t be any empty box.
The axiom states that given any set of mutually disjoint nonempty
sets, there exists at least one set that contains exactly one element in common
with each of the nonempty sets.
In more simple words:
Given a set of non-empty boxes, it is possible to choose an object
from each box.
This point will not seem so frivolous if you ask yourself the
question:
Given infinite number of boxes, would it be possible for me to
choose an item from each one of them?
Physically it should be impossible as we all have a finite time of
living years wherein we can make a choice.
The axiom says you can!
Not physically but mathematically.
You can convert those infinite number of boxes into an infinite
set and assign a function allowing you to operate on that set.
That function would be a choice function which would allow you to
choose an object from each box.
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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