Continuous vs Discrete Variables - Mathematics Stack Exchange
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 …
Proof of Continuous compounding formula - Mathematics Stack …
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 rate (as a
What is the formal definition of a continuous function?
Aug 19, 2022 · The MIT supplementary course notes you linked to give — and use — the following (non-standard) definition: We say a function is continuous if its domain is an interval, and it is continuous …
Understanding definition of a continuous random variable
Jul 27, 2024 · In the continuous case, where random variables can take on values on a continuous scale, the procedure is very much the same. The outcomes of experiments are represented by the …
real analysis - How to show a function is absolutely continuous ...
Aug 5, 2015 · 5 The Cantor function (or the Devil's staircase) provides an example of a continuous function that is not absolutely continuous.
What is the difference between discrete and continuous mathematics?
Some people like discrete mathematics more than continuous mathematics, and others have a mindset suited more towards continuous mathematics - people just have different taste and interests. On the …
Prove that the function $\sqrt x$ is uniformly continuous on $\ {x\in ...
Nov 17, 2013 · @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is uniformly …
Difference between continuity and uniform continuity
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 …
general topology - A map is continuous if and only if for every set ...
Nov 18, 2015 · A map is continuous if and only if for every set, the image of closure is contained in the closure of image
Can a function have partial derivatives, be continuous but not be ...
Sep 18, 2020 · By differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.