complete induction meaning in Hindi

Examples

1. This is the principle of complete induction, which establishes the property of vicious circle.
2. Another proof by complete induction uses the hypothesis that the statement holds for " all " smaller " n " more thoroughly.
3. Complete induction is equivalent to ordinary mathematical induction as described above, in the sense that a proof by one method can be transformed into a proof by the other.
4. Becker was correct that complete induction was needed for assertions of consistency in the form of universally quantified sentences, as opposed to claiming that a predicate holds for each individual natural number.
5. If, on the other hand, P ( " n " ) had been proven by ordinary induction, the proof would already effectively be one by complete induction : P ( 0 ) is proved in the base case, using no assumptions, and is proved in the inductive step, in which one may assume all earlier cases but need only use the case P ( " n " ).
6. These thinkers seem to have maintained a modified observational standpoint for the "'introduction of natural numbers "', for "'the principle of complete induction "'[ . . . ] For these, even for such theorems as were deduced by means of classical logic, they postulated an existence and exactness independent of language and logic and regarded its non-contradictority as certain, even without logical proof.