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==Numbers==

===''Natural numbers''===
Include 0,1,2,3,4,5...

===''Integers''===
Include 0,-1,1,-2,2,-3,3,-4,4...

===''Rational numbers''===
We say that a number is a '''rational number''' if it can be written as n/m, where
n,m are integers and m != 0. In this case n is called '''nominator''' and m '''denominator''' of the rational number.

eg. 1, −5, 3/5 , −9/4...

===''Alphabets''===
A finite collection of symbols. e.g. {1, 2, d, r, $}. An alphabet with two symbols is called a binary alphabet. e.g. {a, b}

A word(string) is a sequence of symbols from an alphabet (say Sigma represents an alphabet).

===''Theorems''===
A statement that, objects satisfy certain properties. It must be true.

==Methods of Proof==

===Dirrect proof method===
If H then C. Solve by logically expanding on definitions.

===Proof by cases method===
This method can be explained as follows. Given a theorem of
the form “If H then C”, the proof by cases method uses the following pattern. Usually the
hypothesis H can be subdivided into several cases, say into three cases call them H1, H2 and
H3. Then one needs to prove that each of these cases implies the conclusion C.

===Proof by contradiction method===
We assume that H is true but C is false.
Then, using a sequence of logical reasoning we derive a contradiction such as 0 = 1.

211Definitions - Revision history

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127.0.0.1 at 00:59, 21 July 2006