# Piecewise function output response interpretation

Piecewise[{{t^2, t <= 0}, {t, t >= 0}}]


Outputs:

t^2   t <= 0
t     t >= 0
0     True


What does the last line of output 0 True mean? Sometimes it also outputs Indeterminate etc. Can someone describe the behavior, constraints, and limitations of this function?

• see Piecewise >> Details: (1) The Subscript[cond, i] are evaluated in turn, until one of them is found to yield True. _ (2) _If all preceding Subscript[cond, i] yield False, then the Subscript[val, i] corresponding to the first Subscript[cond, i] that yields True is returned as the value of the piecewise function. – kglr Mar 19 '15 at 11:15
• .. (3) Piecewise[{{Subscript[val, 1],Subscript[cond, 1]}, ... },val] uses default value val if none of the Subscript[cond, i] apply. The default for val is 0. and (4) Piecewise[{{Subscript[val, 1],Subscript[cond, 1]},{Subscript[val, 2],Subscript[cond, 2]},...s]}] (i.e, single-argument form with no default value is supplied) uses 0 as the default default-value. – kglr Mar 19 '15 at 11:23
• The function returns 0 if neither t >= 0 nor t <= 0. For example, if you define strange /: strange >= 0 = False; strange /: strange <= 0 = False you get a strange value which is neither >=0 nor <= 0. Consequently, if you evaluate your piecewise function with t=strange, you'll get 0 as result. – celtschk Mar 19 '15 at 16:33