Editing Logistic function (section)

===Symmetries===
The logistic function has the symmetry property that

<math display="block">1 - f(x) = f(-x).</math>

This reflects that the growth from 0 when <math>x</math> is small is symmetric with the decay of the gap to the limit (1) when <math>x</math> is large.

Further, <math>x \mapsto f(x) - 1/2</math> is an [[odd function]].

The sum of the logistic function and its reflection about the vertical axis, <math>f(-x)</math>, is

<math display="block">\frac{1}{1 + e^{-x}} + \frac{1}{1 + e^{-(-x)}} = \frac{e^x}{e^x + 1} + \frac{1}{e^x + 1} = 1.</math>

The logistic function is thus rotationally symmetrical about the point (0,&nbsp;1/2).<ref>{{cite book |title=Neural Networks – A Systematic Introduction |author=Raul Rojas |url=http://page.mi.fu-berlin.de/rojas/neural/chapter/K11.pdf |access-date=15 October 2016}}</ref>