In article <firstname.lastname@example.org>, "Ross A. Finlayson" <email@example.com> wrote:
> On Dec 5, 9:05 pm, Virgil <vir...@ligriv.com> wrote: > > In article > > <5312c40d-7490-4838-b49c-573a9f2e1...@i2g2000pbi.googlegroups.com>, > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > On Dec 4, 1:15 pm, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > > <42cabcca-089d-456f-837a-c1d789bda...@jj5g2000pbc.googlegroups.com>, > > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > > > And Heaviside's step is continuous, > > > > > now. For that matter it's a real function. > > > > > > I already said that the step function is a real function, I only > > > > objected to your claim that it was a continuous function. > > > > -- > > > > > Heh, then you said it wasn't, quite vociferously > > > > I objected to it being called continuous. possibly vociferously, but > > your claim that it was continuous deserved vociferous objection. > > > > : you were wrong > > Don't you wish! > > > > , and > > > > > within the course of a few posts wrote totally opposite things. Your > > > memory fails and that's generous, not to mention you appear unable to > > > read three posts back. > > > > > And everybody sees that. > > > > > Then as noted Heaviside's step, a real function, can be simply drawn > > > classically: without lifting the pencil. > > > > Not outside of Rossiana. > > > > http://en.wikipedia.org/wiki/Heaviside_step_function > > The Heaviside step function, or the unit step function, usually denoted > > by H (but sometimes u or ?), is a discontinuous function whose value is > > zero for negative argument and one for positive argument. It seldom > > matters what value is used for H(0), since H is mostly used as a > > distribution. > > > > It's continuous that way. > > > > Not according to Wiki, whom EVERONE here, except possibly WM, trusts far > > more than they trust Ross. > > > > See that phase "discontinuous function"? > > > > Or maybe your as blind as you are thick. > > -- > > > http://en.wikipedia.org/wiki/Heaviside_step_function From wiki: The Heaviside step function, or the unit step function, usually denoted by H (but sometimes u or ?), is a DISCONTINUOUS function whose value is zero for negative argument and one for positive argument. It seldom matters what value is used for H(0), since H is mostly used as a distribution. Some common choices can be seen below. > > * ''H''(0) can take the values zero through one as a removal of the > point discontinuity, preserving and connecting the neighborhoods of > the limits from the right and left, and preserving rotational symmetry > about (0,½).
Except that the value of the Heaviside step function AT zero cannot be chosen so as to make its limit as x increases towards zero though negative values become equal to the limit as x decreases through positive values towards zero, which would be necessary to make the function continuous at zero according to every standard definition of continuity.