if $x\ll 1$ is it safe to assume that $x\ll \frac{1}{2}$

Question

I know that:

if $x\ll 1$ then we can write $\frac{x}{x+1}\rightarrow x$

but is it safe to write $\frac{2x+1}{x+1}\rightarrow 1$?

Yes, usually $<<$ means that the number is positive but near $0$. — Emilio Novati, Mar 22 '15 at 20:29
About your title: Yeah, I think so. (I'm assuming that $\ll$ is used in an informal sense, like $\approx$.) (P.S. Here's a graphing calculator if you want to graph the functions involved: desmos calculator) — Akiva Weinberger, Mar 22 '15 at 20:30

score 0 · Answer 1 · answered Mar 22 '15 at 20:32

0

$\dfrac{2x+1}{x+1} = 2 - \dfrac{1}{1+x} \approx 2 - (1-x)=1+x$

answered Mar 22 '15 at 20:32

DeepSea

I think you mean $2-(1-x)\rightarrow 2-1\rightarrow 1$ because $x<<1$ so $(1-x)\rightarrow 1$ – asdfgg Mar 22 '15 at 20:37

1 Answers1