Examples of using Continuous function in English and their translations into Vietnamese
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It should be a continuous function.
Let be continuous functions not vanishing in the interval and zero elsewhere, such that for every.
Let(X, d) be a metric space and f:X→ X a continuous function.
Find all continuous functions f, g, h, k: R R that.
There is no complication because'f(t)= 3t+ 7' is a continuous function.
Find all continuous functions f, g, h, k: R R that.
This shows the volume of a ball in x dimensions as a continuous function of x.
Let f: X→ Y be a continuous function and suppose Y is Hausdorff.
The most common situation occurs when X is a topological space(such as the real line)and f is a continuous function.
Suppose that$y'(x)$ is continuous function so that$f(x)$ is continuous too.
In 1872,the German mathematician Karl Weierstrass constructed an example of a continuous function that is nowhere differentiable.
Support power-off continuous function, continue printing after incoming calls, no fear of accidental power failure.
A path from a point x to a pointy in a topological space X is a continuous function f from the unit interval[0,1] to X with f(0)= x and f(1)= y.
It says that any continuous function from Sn to Rn maps some pair of antipodal points in Sn to the same point in Rn.
This shows the hypervolume of an(x- 1)-dimensional sphere(i.e., the"area" of the surface of the x-dimensional unit ball)as a continuous function of x.
Although b appears in the equation as a continuous function, we might not know b(t) for all t.
The graph of a continuous function of two variables, defined over a connected open subset of R2 is a topological surface.
Already in 1873, du Bois-Reymond constructed a continuous function whose Fourier series diverges at a point.
What is required may be expressed in mathematical language by saying that theposition of a moving body must be a continuous function of the time.
The mathematician Fourier proved that any continuous function could be produced as an infinite sum of sine and cosine waves.
Quasitopological space Weak Hausdorff space Fixed-point space,a Hausdorff space X such that every continuous function f: X→ X has a fixed point.
For every continuous function f{\displaystyle f}, the following function is continuous and odd: g( x)= f( x)- f(- x){\displaystyle g( x)= f( x)- f(- x)}.
Reputed mathematician Fourier proved in Fourier Analysis that a continuous function can be produced as the infinite sum of the cosine and sine waves.
So if the function is continuous, continuous, continuous, and then it jumps, that disconnect, that would make this function discontinuous, or it would not be a continuous function.
In order for the group law and the topology to interweave well,the group operations must be continuous functions, that is, g• h, and g- 1 must not vary wildly if g and h vary only little.
By the same token, it is impossible for a discontinuous function to have absolutely convergent Fourier coefficients,since the function would thus be the uniform limit of continuous functions and therefore be continuous, .
In mathematics, especially homotopy theory, the homotopy fiber(sometimes called the mapping fiber)[1]is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces f: A→ B. It is dual to the mapping cone.
By passing to orbits under the antipodal action,we then get an induced continuous function h′: R P n→ R P n- 1{\displaystyle h':\mathbb{RP}^{n}\to\mathbb{RP}^{n-1}} between real projective spaces, which induces an isomorphism on fundamental groups.
In mathematics, the Borsuk- Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.
Assume that h: S n→ S n- 1{\displaystyle h: S^{n}\to S^{n-1}}is an odd continuous function with ngt; 2{\displaystyle ngt;2}(the case n= 1{\displaystyle n=1} is treated above, the case n= 2{\displaystyle n=2} can be handled using basic covering theory).