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Real Numbers - Class X
Formulae, Relations, Theorems etc.
Real Numbers
Real Numbers - Combination of Rational and Irrational Numbers. 

Rational Numbers - Numbers which can be represented in the form of p/q where p and q are intergers and Q is not equal to zero. 

Irrational Numbers - (Real) Numbers which cannot be represented in the form of p/q where p and q are intergers and q is not equal to zero. 

Lemma A lemma is a proven statement used for proving another statement.

Algorithm - An algorithm is a series of well defined steps which gives a procedure for solving a type of problem.

Euclid's Division Lemma - Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.

Eulid's Division Algorithm - So, let us state Euclid’s division algorithm clearly.
To obtain the HCF of two positive integers, say c and d, with c > d, follow the steps below:
Step 1 : Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and
r such that c = dq + r, 0 ≤ r < d.
Step 2 : If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
Step 3 : Continue the process till the remainder is zero. The divisor at this stage will
be the required HCF.

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