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A limit of a function

Consider a real valued function defined on reals defined by
-for x<0, the value of the function is 0
-for x greater or equal to 0, the value is 1.
Clearly this function has no limit at 0, being discontinuous.
I wrote the following code
p[x_] := Piecewise[{{ 0, x < 0}, {1, x >= 0}}]
*) Limit[p, x -> 0]    

The result suplied is 1. I do not understand why. 
Please, can someone explain me why is so. Thanks! 
POSTED BY: Marian Muresan
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Please consider the documentation for Limit under "Details and Options"
Limit[expr,x->Subscript[x, 0]] uses the setting Direction->Automatic, which determines the direction from assumptions that have been given, using Direction->-1 as the default. 

You can use the Direction option to choose which direction to take the limit from. So yes, Limit assumes, probably for efficiency, that the limit you ask for exists and it doesn't need to compute both the left and right hand limit.
POSTED BY: Sean Clarke
Thank you!
POSTED BY: Marian Muresan
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