Editing Heaviside step function (section)

==Formulation==
Taking the convention that {{math|''H''(0) {{=}} 1}}, the Heaviside function may be defined as:
* a [[piecewise function]]: <math display="block">H(x) := \begin{cases} 1, & x \geq 0 \\ 0, & x < 0 \end{cases}</math>
* using the [[Iverson bracket]] notation: <math display="block">H(x) := [x \geq 0]</math>
* an [[indicator function]]: <math display="block">H(x) := \mathbf{1}_{x \geq 0}=\mathbf 1_{\mathbb R_+}(x)</math>

For the alternative convention that {{math|''H''(0) {{=}} {{sfrac|1|2}}}}, it may be expressed as:
* a [[piecewise function]]: <math display="block">H(x) := \begin{cases} 1, & x > 0 \\ \frac{1}{2}, & x = 0 \\ 0, & x < 0 \end{cases}</math>
* a [[linear transformation]] of the [[sign function]], <math display="block">H(x) := \frac{1}{2} \left(\mbox{sgn}\, x + 1\right)</math>
* the [[arithmetic mean]] of two [[Iverson bracket]]s, <math display="block">H(x) := \frac{[x\geq 0] + [x>0]}{2}</math>
* a [[one-sided limit]] of the [[atan2|two-argument arctangent]] <math display="block">H(x) =: \lim_{\epsilon\to0^{+}} \frac{\mbox{atan2}(\epsilon,-x)}{\pi}</math>
* a [[hyperfunction]] <math display="block">H(x) =: \left(1-\frac{1}{2\pi i}\log z,\ -\frac{1}{2\pi i}\log z\right)</math> or equivalently <math display="block">H(x) =: \left( -\frac{\log -z}{2\pi i}, -\frac{\log -z}{2\pi i}\right)</math> where {{math|log ''z''}} is the [[Complex logarithm#Principal value|principal value of the complex logarithm]] of {{mvar|z}}

Other definitions which are undefined at {{math|''H''(0)}} include:
* a [[piecewise function]]: <math display="block">H(x) := \begin{cases} 1, & x > 0 \\ 0, & x < 0 \end{cases}</math>
* the derivative of the [[ramp function]]: <math display="block">H(x) := \frac{d}{dx} \max \{ x, 0 \}\quad \mbox{for } x \ne 0</math>
* in terms of the [[absolute value]] function as
<math display="block"> H(x) =  \frac{x + |x|}{2x}</math>