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Base case may refer to: Base case (recursion) , the terminating scenario in recursion that does not use recursion to produce an answer Base case (induction) , the basis in mathematical induction, showing that a statement holds for the lowest possible value of n
A simple base case (or cases) — a terminating scenario that does not use recursion to produce an answer; A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or
Short-circuiting the base case, also known as arm's-length recursion, consists of checking the base case before making a recursive call – i.e., checking if the next call will be the base case, instead of calling and then checking for the base case. Short-circuiting is particularly done for efficiency reasons, to avoid the overhead of a ...
The first, the base case, proves the statement for = without assuming any knowledge of other cases. The second case, the induction step , proves that if the statement holds for any given case n = k {\displaystyle n=k} , then it must also hold for the next case n = k + 1 {\displaystyle n=k+1} .
Most recursive definitions have two foundations: a base case (basis) and an inductive clause. The difference between a circular definition and a recursive definition is that a recursive definition must always have base cases, cases that satisfy the definition without being defined in terms of the definition itself, and that all other instances in the inductive clauses must be "smaller" in some ...
It may prove key in determining whether the "base case" Powell pointed to of quarter-point rate cuts at the Fed's remaining two meetings this year remains intact, or the debate gets tilted towards ...
In case h ≤ g, the whole tree extends over 1 + g generations and shows p + q + 1 ≤ 2 g + 1 − 1 persons by similar reasoning, i.e. the whole tree satisfies the property in this case also. Hence, by structural induction, each ancestor tree satisfies the property. As another, more formal example, consider the following property of lists :
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