To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") simultaneously …

Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a piecewise continuous

May 10, 2019 · Of course, the CDF of the always-zero random variable $0$ is the right-continuous unit step function, which differs from the above function only at the point of discontinuity at $x=0$.

Jan 27, 2014 · To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on R R but not uniformly continuous on R R.

In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?

Dec 28, 2015 · A continuous random variable is a random variable with a continuous cumulative distribution function F F. Typically the range of a continuous random variable is R R, [0, ∞) [0, ∞), or …

A function f: [0, 1] → R f: [0, 1] → R is called singular continuous, if it is nonconstant, nondecreasing, continuous and f′(t) = 0 f (t) = 0 whereever the derivative exists. Let f f be a singular continuous …

Dec 26, 2025 · Let (X, n) (X, n) be normed space and B B a basis (by basis I mean a set of vector such that every vector in X can be expressed in an essentially unique way as a finite linear combination of …

Jan 13, 2012 · the difference is in definitions, so you may want to find an example what the function is continuous in each argument but not jointly

Oct 28, 2024 · Integral of non-continuous function Ask Question Asked 1 year, 2 months ago Modified 1 year, 2 months ago