# Base Case

Base case can refer to:

• A case of a recursive definition that is not defined in terms of itself
• The basis in mathematical induction, showing that a statement holds when n is equal to the lowest value that n is given in the question (usually, n = 0 or n = 1)

### Other articles related to "base cases, base case, cases, case, base":

Proofs Involving The Addition Of Natural Numbers - Proof of Commutativity
... First we prove the base cases b = 0 and b = S(0) = 1 (i.e ... The base case b = 0 follows immediately from the identity element property (0 is an additive identity), which has been proved above a + 0 = a = 0 + a ... Next we will prove the base case b = 1, that 1 commutes with everything, i.e ...
Recursive Call - Implementation Issues - Short-circuiting The Base Case - Depth-first Search
... The standard recursive algorithm for a DFS is base case If current node is Null, return false recursive step otherwise, check value of current node ... In terms of the standard steps, this moves the base case check before the recursive step ... Alternatively, these can be considered a different form of base case and recursive step, respectively ...
Recursive Call - Implementation Issues
... actual implementation, rather than a pure recursive function (single check for base case, otherwise recursive step), a number of modifications may be made, for ... These include Wrapper function (at top) Short-circuiting the base case, aka "Arm's-length recursion" (at bottom) Hybrid algorithm (at bottom ... to reduce the overhead of recursion in small cases, and arm's-length recursion is a special case of this ...
Corecursion
... deductively), working on large data (more properly, data further from a base case) by breaking it into smaller data and repeating until one reaches a base ... to operate on arbitrarily complex data, so long as it can be reduced to simple data (base cases), corecursion allows programs to produce arbitrarily complex and potentially infinite data ... Where recursion may not terminate, never reaching a base state, corecursion starts from a base state, and thus produces subsequent steps deterministically, but the result may be ...
Mathematical Induction - Description
... The proof consists of two steps The basis (base case) showing that the statement holds when n is equal to the lowest value that n is given in the question ... The choice between n = 0 and n = 1 in the base case is specific to the context of the proof If 0 is considered a natural number, as is common in the fields of combinatorics and ... on the other hand, 1 is taken as the first natural number, then the base case is given by n = 1 ...

### Famous quotes containing the words case and/or base:

When a thing is said to be not worth refuting you may be sure that either it is flagrantly stupid—in which case all comment is superfluous—or it is something formidable, the very crux of the problem.
Miguel de Unamuno (1864–1936)

Then must you speak
Of one the lov’d not wisely but too well;
Of one not easily jealous, but, being wrought,
Perplex’d in the extreme; of one whose hand,
Like the base Indian, threw a pearl away
Richer than all his tribe;
William Shakespeare (1564–1616)