The following three steps are used in recursive definition
Some basic words are specified in the language.
Rules for constructing more words are defined in the language.
No strings except those constructed in above, are allowed to be in the language.
Example
Defining language of INTEGER
Step 1: 1 is in INTEGER.
Step 2: If x is in INTEGER then x+1 and x-1 are also in INTEGER.
Step 3: No strings except those constructed in above, are allowed to be in INTEGER.
Example
Defining language of EVEN
Step 1: 2 is in EVEN.
Step 2: If x is in EVEN then x+2 and x-2 are also in EVEN.
Step 3: No strings except those constructed in above, are allowed to be in EVEN.
Example
Defining the language factorial
Step 1: As 0!=1, so 1 is in factorial.
Step 2: n!=n*(n-1)! is in factorial.
Step 3: No strings except those constructed in above, are allowed to be in factorial.
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