Re: Step Function

In article <GiIOe.3107$x43.1378149@xxxxxxxxxxxxxxxxxx>,
Hsuan-Yeh Chang <hsuanyeh@xxxxxxxxx> wrote:
>Dear All,
>
>Let S(x) be a step function,
>
>S(x) = / 0, x < 0; and
> |
> \ 1, x >= 0.
>
>where x is a real number.
>
>Suppose x is a two dimensional vector x = a i + b j
>where a, b are two real numbers, while i, j are the unit
>vectors of the x, y coordinates, respectively.
>
>Is S( a i + b j ) = S(a)S(b) ??

Huh?

Your S is defined to be a function of real variable. If you want to
define a new, DIFFERENT function whose domain is the set of ordered
pairs, you can do so; you can even define it in terms of your old,
1-variable function. But you cannot "deduce" the definition of this
putative function from the definition of the 1-variable one. You can
make many definitions.

--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
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Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.