Editing Mathematical induction (section)

== Description ==
The simplest and most common form of mathematical induction infers that a statement involving a [[natural number]] {{mvar|n}} (that is, an integer {{math|''n'' ≥ 0}} or 1) holds for all values of {{mvar|n}}. The proof consists of two steps:
# The '''{{vanchor|base case}}''' (or '''initial case'''): prove that the statement holds for 0, or 1.
# The '''{{vanchor|induction step}}''' (or '''inductive step''', or '''step case'''): prove that for every {{mvar|n}}, if the statement holds for {{mvar|n}}, then it holds for {{math|''n'' +&thinsp;1}}. In other words, assume that the statement holds for some arbitrary natural number {{mvar|n}}, and prove that the statement holds for {{math|''n'' +&thinsp;1}}.

The hypothesis in the induction step, that the statement holds for a particular {{mvar|n}}, is called the '''induction hypothesis''' or '''inductive hypothesis'''. To prove the induction step, one assumes the induction hypothesis for {{mvar|n}} and then uses this assumption to prove that the statement holds for {{math|''n'' +&thinsp;1}}.

Authors who prefer to define natural numbers to begin at 0 use that value in the base case; those who define natural numbers to begin at 1 use that value.