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 …

Mar 4, 2026 · I was trying to formalize some things about string motion in physics so I could answer more general questions about it and then I got to a point as to see the limit written below. I then …

Jul 22, 2010 · The cardinality is at most that of the continuum because the set of real continuous functions injects into the sequence space $\mathbb R^N$ by mapping each continuous function to its …

More frustratingly, the people giving the answers make bigger mistakes or have bigger confusions about continuity than the person asking for continuity: for a detailed explanation on how to show that the …

The space of bounded continuous functions is not separable Ask Question Asked 13 years, 4 months ago Modified 3 months ago

You'll find topological properties with indication of whether they are preserved by (various kinds of) continuous maps or not (such as open maps, closed maps, quotient maps, perfect maps, etc.). For …

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 …

Mar 7, 2013 · 22 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it like …

Nov 29, 2017 · The sum of continuous functions are continuous, and the sum of an increasing function with a strictly increasing one is strictly increasing. As in the proof that $\text {c}$ is not absolutely …

Continuous time models are useful when the dynamics you are interested in are fine enough to be approximated as a continuous process. Moreover, it is a common misconception that somehow …