There are other ways a function can be a continuous extension, but probably the most basic way (and likely about the only way you'll see in elementary calculus) is that you have a function …

Following is the formula to calculate continuous compounding. A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest …

May 10, 2019 · This fact is useful to resolve this natural question: Let $\{X_i\}_{i=1}^{\infty}$ be i.i.d. random variables uniform over $[-1,1]$.

Oct 15, 2016 · A piecewise continuous function doesn't have to be continuous at finitely many points in a finite interval, so long as you can split the function into subintervals such that each …

If we restrict ourselves to the case of functions which are continuous on the compact interval $[0,1]$, this is in the sense of (classical) Wiener measure, but is likely well beyond the scope …

Sep 10, 2018 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Jan 8, 2017 · continuous spectrum $\sigma_c(T)$: (R2) isn't satisfied, but (R1) and (R3) are satisfied. residual spectrum $\sigma_r(T)$: (R3) isn't satisfied, (R1) is satisfied, (R2) - doesn't …

Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider …

Jul 21, 2020 · Is the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines …

Jan 27, 2014 · I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. …