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 …

In fact the author's statement is not clear, because by stating "is not uniformly continuous" one is assuming the function is in some underlying domain already. If it is an close interval with no singular …

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

Jul 28, 2017 · I have heard of functions being Lipschitz Continuous several times in my classes yet I have never really seemed to understand exactly what this concept really is. Here is the definition. …

Then the theorem that says that any continuous function on a compact set is uniformly continuous can be applied. The arguments above are a workaround this.

Apr 4, 2022 · Does there exist a continuous bijection from $(0,1)$ to $[0,1]$? Of course the map should not be a proper map.

Jun 12, 2016 · Basic real analysis should be a source of at least some intuition (which is misleading at times, granted). Can you think of some compact sets in $\mathbf R$? Are continuous functions on …

Jun 11, 2025 · 6 "Every metric is continuous" means that a metric $d$ on a space $X$ is a continuous function in the topology on the product $X \times X$ determined by $d$.

Oct 11, 2017 · To prove that every rational function is continuous (needless to add "on its domain": it would be redundant, in view of the definition of continuity), knowing that every polynomial is, you just …

Jan 21, 2014 · The argument function has domain $ℂ\setminus\ {0\}$ and values in $ℝ/2\piℝ$ (a space homeomorphic to a circle) and as such, it is continuous. It's not well-defined as a function to $ℝ$.