Mathematical Induction

SYNOPSIS

• The key basis for mathematical thinking is deductive reasoning.
  
  
• Deduction: When we have to prove a statement, often called a conjecture or a theorem in mathematics, valid deductive steps are derived and a proof may or may not be established, i.e. deduction is the application of a general case to a particular case.
  
  
• Inductive reasoning depends on working with each case and developing a conjecture by observing incidences till we have observed each and every case.
  
  
• Induction means generalisation from particular cases or facts.
  
  
• The principle of mathematical induction is one such tool which can be used to prove a wide variety of mathematical statements.
  
  
• Each such statement is assumed as P(n) associated with a positive integer n, for which the correctness for the case n = 1 is examined. Assuming the truth of P(k) for some positive integer k, the truth of P(k + 1) is established.