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What is the value of \$u(t)\$ for \$t=0\$?

we know,

\$u(t)=1\$, for \$t \gt 0\$

\$u(t)=0\$, for \$t \lt 0\$

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    \$\begingroup\$ Many of these questions are a better fit for mathematics.SE as they are pure math. We have kept many here and answer, but things like this are a pure mathematical convention. This definition of the step function is clearly poor, it should define the value at 1, there is no way for you to know without someone telling you what they expect to be correct. '1' is the standard EE answer. \$\endgroup\$
    – Kortuk
    Feb 24 '13 at 7:50
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It's all a matter of convention.

In mathematics they often define \$u(0) = \frac{1}{2}\$, which is called the half-maximum convention:

enter image description here

If you only want values of 0 and 1 (and not the \$\frac{1}{2}\$) then they usually define \$u(0) = 1\$, which is called the discrete form:

\$u(t)=\begin{cases} 0, & n < 0, \\ 1, & n \ge 0 \end{cases}\$

More information about this function is here: http://en.wikipedia.org/wiki/Heaviside_step_function

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    \$\begingroup\$ Yeah, in EE we always consider it 1 for DSP purposes. Having a 1/2 point would make lots of real world things harder. \$\endgroup\$
    – Kortuk
    Feb 24 '13 at 7:48
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It doesn't matter. Arguing about it is pointless. Pick whatever is convenient from 0 to 1 and move on.

Note that I'm saying this within the context of the being a engineering site. The condition only exists for a infinitely short time, so as long as the value is not infinite, it will have no effect on any answer.

If you had asked about a discrete function, such as we get by periodic sampling or producing periodic outputs, then this does matter since the value will persist for the time of one sample and therefore will effect the answer. However, you asked a theoretical and more pointless question, so there is no reason to get into this further.

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