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 values that you can count while continuous variables are those that you can measure such as weight or height.
Hence $f$ is continuous in $x_0 \in \mathbb {Q}$ and since this calculation holds for any such $x_0 \in \mathbb {Q}$, we have that $f$ is continuous on $\mathbb {Q}$.
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. $\left...
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 square root function is continuous, here is a Pdf file that gives a detailed example.
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
Let $X$ be a metric space , $d$ is the metric , show that $d$ is a continuous function from $X\times X$ to $R$. I think the definition is all we need , but I just don't know where to start , can anyone help me.
Does there exist a continuous bijection from $(0,1)$ to $[0,1]$? Of course the map should not be a proper map.
real analysis - Continuous bijection from $ (0,1)$ to $ [0,1 ...
If $x\in A$ and $y\in B$, we use the fact that a uniformly continuous function extends by continuity to the shadow (standard part) $c=\text {st} (x)$. Then the $h (x)\approx h (c)\approx h (y)$ and therefore the extended function is uniformly continuous.