What is deductive and inductive proof?

Deductive proof: A deductive proof consists of a sequence of statement whose truth leads us from some initial statement (hypothesis or given statement) to a conclusion statement. Each step of a deductive proof MUST follow form a given fact or previous statements ( or their combinations) by an accepted logical principal. The theorem that is proved when we go form a hypothesis H to a conclusion C is the statement “ if H then C”. We say that C is deduced from H.

induction means, proof something for all natural numbers by first proving that it is true for 0, and that if it is true for n (or sometimes, for all numbers up to n), then it is true also for n+1.

An inductive proof has three parts:- Basis case- Inductive hypothesis- Inductive step.
Suppose a statements P9n) about a non-integer n.
The principle of mathematical induction is that P(n) follows from
(a) P(0), and
(b) P(n-1) implies P(n) for n ≥ 1.
Condition (a) in the inductive proof is called the basis, and condition (b) is called the inductive step. The left hand side of (b), that is P(n-1) is called inductive hypothesis.