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# IntegerPart

 IntegerPart[x]gives the integer part of x.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• IntegerPart[x] in effect takes all digits to the left of the decimal point and drops the others.
• IntegerPart[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number.
• For exact numeric quantities, IntegerPart internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable \$MaxExtraPrecision.
• IntegerPart applies separately to real and imaginary parts of complex numbers.
Find the integer part of a real number:
Find the integer part of a real number:
 Out[1]=
 Scope   (4)
Use exact numeric quantities:
Manipulate IntegerPart symbolically:
Evaluate an integral:
Use with negative arguments:
Use with complex-number arguments:
IntegerPart can deal with real-valued intervals:
Infinite arguments give symbolic results:
Series expansion:
 Applications   (8)
Iso-curves become full-dimensional regions for piecewise constant functions:
Fibonacci numbers:
Implement a divide-and-conquer-type recursion relation:
Find the 1000000 digit of the fraction 1/99^2 in base 10:
Compare with RealDigits functionality:
Find the day of the week in the Gregorian calendar:
Birthday of Leonard Euler:
Compare with DateString:
Implement the Frisch continuous-but-nowhere-differentiable function:
Simplify expressions containing IntegerPart:
Symbolically expand for complex arguments:
IntegerPart is idempotent:
Use PiecewiseExpand to canonicalize:
Reduce equations containing IntegerPart:
Numerical decision procedures with default settings cannot simplify this expression:
Use Simplify to resolve:
Machine-precision numericalization of IntegerPart can give wrong results: