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 …

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 rate (as a …

Dec 18, 2025 · I was recently going through General Topology by N. Bourbaki, and found the following definition of topological groups acting continuously on topological spaces (slightly rephrased) : A …

Dec 26, 2025 · (See e.g. Linear functional is continuous $\implies$ it is bounded for a proof that a continuous linear functional on a normed vector space must be bounded. This is also on Wikipedia.)

Jan 5, 2016 · As such, $\arctan$ is continuous. If you define $\arctan$ by integrals or power series the result is immediate (the first by the Lipshitz continuity of the indefinite integral and the second from …

Proving the inverse of a continuous function is also continuous Ask Question Asked 12 years, 4 months ago Modified 8 years, 3 months ago

Jan 8, 2017 · The reason one refers to this as "continuous spectrum" Historically had nothing to do with continuity; such spectrum was found to fill a continuum, rather than being discrete.

Aug 4, 2022 · Isn't this violating the definition of continuous stochastic process or is it that I have to keep $\omega$ constant throught out the process ? Also, is $\omega$ in the definition of continuous …

Apr 3, 2022 · So you can have continuous functions defined over rationals; but the rationals are not a continuum. Why not? The notion of a continuum has its roots in geometry, and -- in the barest …

The proofs I've seen of the fact that open sets have open preimages either use the fact that continuous functions map limit points to limit points, or they use a completely topological proof. Is there a more …