Throughout this book, an item with a label 2.1.3 means the 3-rd item of the 1-st section of
Chapter 2. While defining a new term or a new notation we shall use bold face letters. The
symbol := is used at places we are defining a term using equality symbol. A symbol !! at the
end of a statement reminds the reader to verify the statement by writing a proof, if necessary.
We assume that the reader is familiar with the very basic of counting. A reader who is not,
may avoid the counting items in the initial parts till we start to discuss counting.
We also assume that the reader is familiar with some very basic definitions involving sets.
This book is written with the primary purpose of making the reader understand the discussion.
We do not intend to write elaborate proofs for the reader to read, as there is no end to elaboration.
We request the reader to take each statement in the book with the best possible natural meaning.
Here are a few collected quotes, mainly intended to inspire the authors.
The value of a college education is not the learning of many facts but the training of
the mind to think.
Imagination is more important than knowledge. For knowledge is limited, whereas
imagination embraces the entire world, stimulating progress, giving birth to evolution.
It is, strictly speaking, a real factor in scientific research.
Everything should be made as simple as possible, but no simpler.
Do not worry about your difficulties in Mathematics. I can assure you mine are still