e , 2x1+ 5 = 2x2 + 5
⇒
2x1+ 5 – 5 = 2x2 + 5 – 5  (adding the same quantity on both sides)
Rationalised 2023-24
PROOFS IN MATHEMATICS
189
⇒
2x1+ 0 = 2x2 + 0
⇒
2x1 = 2x2 (using additive identity of real number)
⇒
1
2
2 x  =
2
2
2 x  (dividing by the same non zero quantity)
⇒
x1 = x2
Hence, the given function is one-one (ii) Mathematical Induction
Mathematical induction, is a strategy, of proving a proposition which is deductive in
nature The whole basis of proof of this method depends on the following axiom:
For a given subset S of N, if
(i)
the natural number 1 ∈ S  and
(ii)
the natural number k + 1 ∈ S whenever k ∈ S, then S = N