s**e
发帖数: 1834 | 1 I am a little confused about the difference between these 2 math symbols
"$\sim$" and "$\approx$".
To give an example, let f1(x) = x, and f2(x)=x + x^2, f3(x)=2x.
And we consider x-->0 only.
I think both expression "f1(x) \sim f2(x)" and "f1(x) \approx f2(x)" are
correct. But what about f1(x) vs f3(x)? Should we use "f1(x) \sim f3(x)" or
"f1(x) \approx f3(x)"? |
v**i
发帖数: 50 | 2 It seems that $\approx$ is never used in these discussions of limits. When $
\lim f(x)=0$ and $\lim g(x)=0$, the meaning of $f(x)\sim g(x)$ is that
\lim_{x} f(x)/g(x)=1.
Thus you can write $f1(x)\sim f2(x)$, but neither $f1(x)\sim f3(x)$ nor $f2(
x)\sim f3(x)$. |
s**e
发帖数: 1834 | 3 Thanks for the reply. Since f1(x) and f3(x) "has the same order", then is
there a symbol that can be use btw "f1(x) vs f3(x)"?
Say, we can write "2x \sim O(x)".
$
f2(
【在 v**i 的大作中提到】
: It seems that $\approx$ is never used in these discussions of limits. When $
: \lim f(x)=0$ and $\lim g(x)=0$, the meaning of $f(x)\sim g(x)$ is that
: \lim_{x} f(x)/g(x)=1.
: Thus you can write $f1(x)\sim f2(x)$, but neither $f1(x)\sim f3(x)$ nor $f2(
: x)\sim f3(x)$.
|
B********e
发帖数: 10014 | 4 I use $f1\sim f2$ as well as $f1\sim f3$ although i use $\approx$ in calculu
s class sometime :)
$
f2(
【在 v**i 的大作中提到】
: It seems that $\approx$ is never used in these discussions of limits. When $
: \lim f(x)=0$ and $\lim g(x)=0$, the meaning of $f(x)\sim g(x)$ is that
: \lim_{x} f(x)/g(x)=1.
: Thus you can write $f1(x)\sim f2(x)$, but neither $f1(x)\sim f3(x)$ nor $f2(
: x)\sim f3(x)$.
|
B********e
发帖数: 10014 | 5 i guess when you use big O, you always want to say "...=O(...)"
【在 s**e 的大作中提到】
: Thanks for the reply. Since f1(x) and f3(x) "has the same order", then is
: there a symbol that can be use btw "f1(x) vs f3(x)"?
: Say, we can write "2x \sim O(x)".
:
: $
: f2(
|
