advanced math theory

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical I..

Mathematical Induction..

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Scientific Notation - Notation of large number in terms of exponential form, 10 raised to required value. It is also a standart notation representation as " p x 10 q ". where 'p' and 'q' are any integer..

Principle of Mathematical Induction (PMI) - (i) P(1) is true (ii) P(r) is true P(r+1) is tr..

If P(n) is a statement (n N); such that 1. P(1) is true and 2. truth of P(k) implies the truth of P(k+1), then by the principle of mathematical induction (P.M.I.), the statement P(n) is true for n ..

Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a..

(i) P(1) is true (ii) P(r) is true P(r+1) is tr..

Conclusion - Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+1 whenever it holds for n =..

Question 1 - Question: Define an even number. Answer: A number which is divisible by 2 is called an even numbe..