An example of a function discontinuous everywhere
fa(x) = 1 , if x belongs to set a
fa(x) = 0 if x does not belong to set a
The a is a subscript here. This function is called the 'Indicator function' and everywhere discontinuous.
to hold the staples in place so they can be forced through the paper without flying around everywhere
Science is everywhere because nature surrounds us, organisms are everywhere, and even though you don't see tiny organisms, its everywhere.
biomass energy is located everywhere on this planet!
Matter is everywhere. Where there is no matter , it is a vacuum. You as a biological organism are matter.
The mass of an object remains the same everywhere in the universe.
Weistrass function is continuous everywhere but not differentiable everywhere
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
A cubic function is a smooth function (differentiable everywhere). It has no vertices anywhere.
No.
Yes, a Fourier series can represent a function that is discontinuous. While the series converges to the function at points of continuity, at points of discontinuity, it converges to the average of the left-hand and right-hand limits. This phenomenon is known as the Gibbs phenomenon, where the series may exhibit oscillations near the discontinuities. Despite these oscillations, the Fourier series still provides a useful approximation of the function.
The unit step function is also known as the Dirac delta function. It can be thought of as a function of the real line (x-axis) which is zero everywhere except at the origin (x=0) where the function is infinite in such a way that it's total integral is 1 - hence the use of the word 'unit'. The function is not a strict function by definition in that any function with the properties as stated (0 everywhere except the origin which by definition has a limit tending to 0), must therefore also have an integral of 0. The answer is therefore zero everywhere except at the origin where it is infinite.
That means that either the function is equal to zero everywhere (y = 0), or it is the exponential function (y = ex).
It is; everywhere except at x = 0
it is to clip paper so that the paper would not be flying around everywhere
Cells are usually round without corners only curves.
Υou show that it is continuous in every element of it's domain.
to hold the staples in place so they can be forced through the paper without flying around everywhere