Dec 14, 2025 · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those …

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 $\mathbb R$ but not uniformly …

Nov 9, 2024 · I learned a theorem that if $f$ is continuous and bijective then $f^ {-1}$ is continuous. I went online to search for a proof and saw a really long proof in this link.

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 …

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 …

As you have it written now, you still have to show $\sqrt {x}$ is continuous on $ [0,a)$, but you are on the right track. As @user40615 alludes to above, showing the function is continuous at each point in the …

Oct 28, 2024 · Integral of non-continuous function Ask Question Asked 1 year, 3 months ago Modified 1 year, 3 months ago

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 21, 2012 · I found this comment in my lecture notes, and it struck me because up until now I simply assumed that continuous functions map closed sets to closed sets. What are some insightful …

Apr 1, 2025 · It's more correct to say that he proved Jensen's Inequality (with arbitrary real weights) for functions which are midpoint convex and continuous. Of course, Jensen's Inequality with two …