Hi guys, sorry about that but maybe I magnificent the subject and I understand it wrongly so I need to understand it well.
what does it mean in math that X dependence to y? and if not dependence to y, what does that mean mathematics?!
to be more clear, how dependency and not dependency represented in aspects of math? and if not dependent then not dependent and it's concrete..... like black or white yeah? no more choices ..
First, we have to figure out what the proper English for your question would be; when you ask about what is largely a language issue, language errors tend to get in the way. Here is my attempt to rewrite this as it
might really be intended (that is, this is a guess):
What does it mean in math that x depends on y? and if x does not not depend on y, what does that mean mathematically?!
To be more clear, how are dependence and non-dependence represented in aspects of math? And are these the only possibilities, so that a variable is either dependent or not dependent, and it's concrete..... like black or white? No other choices?
(I'm making no attempt to figure out what you meant by using "magnificent" as a verb. I presume that was just a slip.)
When we say that (within a particular problem)
x depends on y, we are saying that we are taking y to be the
independent variable, which is considered to be assigned a value without reference to the other, and x to be the
dependent variable, meaning nothing more than that x is
being thought of as a function of y, that is x = f(y) for some function f.
There are other possibilities; we could have taken x and y to be
both independent, and something else to depend on them, or each might
depend on some other variable.
Also, this says nothing inherent about either variable; it reflects only the
relationship we are thinking about. In particular, would could often think of either variable as dependent on the other; for example, in a graph, we could choose to make height a function of arm length, or arm length a function of height. (In reality, neither is determined by the other -- both are determined by other factors.)
but I can also write y=f(x)=constant then what? is y depend on x or not? the syntax y=f(x) still telling you that y is related to x .. ! but might be f(x)=const as?!
If the
function happens to be a constant, then all that says is that
y is itself constant. We are still calling y the
dependent variable, but that doesn't mean much, as the dependence is trivial. We can at the same time say that y is
independent of x, which is not the same as being the independent variable. Again, dependence says nothing about the variable, or even about any real relationship between them, but only about
how we are choosing to look at them.
As an example, consider the famous experiment in which objects are dropped from a fixed height to see which hit the ground fastest. We are trying to determine the dependence of fall time on mass; if it turns out that the time is always the same (independent of mass), then we are finding that this is a constant function. In our calculations, we are
treating mass as the independent variable, and determining that the dependent variable is in fact constant. We are then finding that in reality
time is independent of mass.
Ultimately, I think you need to ask these questions of someone who speaks your language, quoting actual problems in the original language, and asking how that language is used. Your language may have different ways to express these ideas, so what we say about English may be irrelevant to you. Optionally, you could
quote the original to us
in that language, in such a form that we can use Google or other means to translate it ourselves, and if we want to take the time, try to answer you. To do more is probably a waste of your time and ours.