Difference between continuity and uniform continuity

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

2025 Jan 29

What is a continuous extension?

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")

2024 Jun 01

probability theory

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 $x=0$.

2024 Apr 18

Continuous versus differentiable

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...

2026 Jan 15

Continuous vs Discrete Variables

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

2024 Nov 20

Why absolute-value function is not a continuous function

You are confusing "piecewise" with "step". The absolute value function has a piecewise definition, but as you and the text correctly observe, it is continuous. Informally, the

2025 Apr 13

Absolutely continuous functions

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

2024 Mar 31

Discrete vs Continuous vs Random Variables

Typically the range of a continuous random variable is $mathbb {R}$, $ [0,infty)$, or some interval $ [a,b]$. Examples of continuous random distributions are the normal

2025 Sep 07

What''s the difference between continuous and piecewise

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

2024 Jul 09

Proof of Continuous compounding formula

12 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

2025 Jun 21

View/Download Continuous discharge current of energy storage cabinet battery [PDF]

PDF version includes complete article with source references. Suitable for printing and offline reading.