Show me a function f(x) such that
Actually this really more of a question I have than a challenge. I do have a solution but am challenging inquisitively. If that gets on everyone's nerves just kindly ignore this and I will post it later on as a challenging inquisition rather than an inquisitive challenge.
The roots of y in the equation (which is the equation plotted in the attachment)
are and
So, i.e.
(The limit was as x goes to infinity, not 0. REALLY SORRY about that.)
and yet the other root of y euals this limit, equals -1. So, can't it be said that the function y equals its limit?
Thanks. And yet this is true, if it is true that AND
And yet it is untrue, as you point out, for the very same reason. In other words this is a logical contradiction. And a contradiction on two counts: 1) because one root is a constant, and the other is a function, and yet both roots must be defined at the outset as EITHER a function OR a constant, not both; and 2) because the domain of one root is undefined or mathematically meaningless vis-a-vis the domain of the other root (because it involves 1/infinity).
How does one resolve the contradiction? How do you qualify "AND" to resolve it?
Any continuous function has the property that , that's the definition of "continuous". It is true for all for any function, f, that is continuous for all real numbers.
That is NOT true for because that function is not defined, and so not continuous, at x= 0.
I have no idea what you are trying to say.
Surely, the problem is rather that I am not grasping the full import of what you are all saying. So, thanks for your patience and comments. I will ruminate on the input I've received in this thread and will no doubt eventually come around to a proper understanding (both of what you're saying and of what I'm trying to get at).