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 …
Absolutely continuous functions - Mathematics Stack Exchange
Sep 5, 2012 · This might probably be classed as a soft question. But I would be very interested to know the motivation behind the definition of an absolutely continuous function. To state "A real valued …
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 …
probability theory - Why does a C.D.F need to be right-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 $x=0$.
What does it mean for a function to be continuous on its domain?
Feb 8, 2018 · Functions that are not continuous do not exist for every x value over the domain. For example if a function is defined near an open interval (the circle that is not shaded on a graph) then …
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 …
real analysis - Are Continuous Functions Always Differentiable ...
Oct 26, 2010 · An interesting fact is that most (i.e. a co-meager set of) continuous functions are nowhere differentiable. The proof is a consequence of the Baire Category theorem and can be found (as an …
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 …
Proving the inverse of a continuous function is also continuous
Proving the inverse of a continuous function is also continuous Ask Question Asked 12 years, 5 months ago Modified 8 years, 4 months ago