What is the formal definition of a continuous function?
Aug 19, 2022 · The function ƒ does not have a removable discontinuity at x = 0. On the other hand, this document I found on the MIT Math portal, has this to say about that same function …
What does "continuous" mean on functions over the rationals?
Jul 11, 2020 · The $\epsilon$ - $\delta$ definition of limit, and of continuity, make sense in the rationals. Many (but not all) of the proofs you may see about limits and continuity in your …
But what is a continuous function? - Mathematics Stack Exchange
Jan 30, 2019 · I am confused about "continuous function" term. What really is a continuous function? A function that is continuous for all of its domain or for all real numbers? Let's say: …
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 …
What is the difference between discrete and continuous …
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 …
smooth functions or continuous - Mathematics Stack Exchange
Feb 8, 2022 · A function can therefore be said to be smooth over a restricted interval such as or . The number of continuous derivatives necessary for a function to be considered smooth …
measure theory - What does it mean to be an $L^1$ function ...
Your friend's definition misses out on some subtleties, but it's basically correct. I'm afraid a rigorous definition cannot avoid Lebesgue integration and measure theory.
Sequential definition of continuity: What does "all sequences mean
Apr 21, 2021 · How does the topologist's sine curve fit with this definition? This function is not continuous at $a=0$. The reason is that we can find two different sequences which both …
What's the difference between continuous and piecewise …
Oct 15, 2016 · As such, I'm confused by what a piecewise continuous function is and the difference between it and a normal continuous function. I'd appreciate it if someone could …
sequences and series - Are linear functions always continuous ...
Jul 30, 2019 · I don't think this is a question on the technical definition of continuity. It sounds more like the OP is thinking of the non-technical dichotomy of 'continuous' vs. 'discrete', e.g., …