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Is there a name to describe a set of functions that when taken together cover all possible input and output values, but without overlapping?
Like for example, one function a(x) > 0 that applies to x > 0 and b(x) < 0 that applies to x < 0? A name for the both a and b together?
What I am working on is rules that say:
when A is known then set B to some function of A
when A is unknown then set B to unknown
I want to say that the two rules must constitute a complete set, but I wondered if there is a technical term for this?
Simultaneous equations?
Boolean logic?
In maths, I would call it a discrete function of x that covers the real space. Don't know if the following pic example will show.
My parter who is an Engineer would call it a discrete switch.
Why do you need to know, as in who/what is this for?
(Also you need an x=0 to cover all of the real space and I don't think you mean a(x)>0 but a(x>0)? In which case define f(x) = {a(x), x>=0, b(x), x<0. Then define a and b on the next line. Clearer that way.).
Should have also said, I presume you mean a(x>0) rather than a(x)>0. You can define f(x) in terms of a(x) and b(x) first. Then describe a and b.
If the gap at x=0 was covered I'd have called it a continuous set of functions. But IANAM and they are very pedantic about definitions.
Piecewise Function
http://mathworld.wolfram.com/PiecewiseFunction.html
but like above, you'll be wanting to specify 0 (either explicitly as a single point, or by making one of the other operators either <= or >=, or perhaps by formally excluding it as an input)
I want the name for the whole complimentary set. I want to say these rules/functions together cover all eventualities without overlap. I thought there might be a mathematical term for it but maybe it's a logical or computery one.
Yeah, in more of a computational / coding sense, it's just a case switch or logical switch that covers all possibilities in the input. No idea if there is a term for that in the software development community.
I want the name for the whole complimentary set. I want to say these rules/functions together cover all eventualities without overlap. I thought there might be a mathematical term for it but maybe it’s a logical or computery one.
There is, Andy the Rocketeer told you?
Piecewisefunction
You need a collective noun, I suggest you use 'bobbins' and just bluff your way..
I present the bobbins of functions which define the problem space....
Piecewise is good - I'll go for piecewise continuous function.