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Let's say if I know that $V \gg x^2$,

I know that for example:

$x^2 +V\sim V$,

however, if I have

$x^2 - V$,

can I still say that this equals

$x^2 - V\sim -V$?

Basic intuition tells me this must be so, based on taking numerical examples, i.e., if $1000 \gg 1$, then $1 - 1000 = -999 \sim -1000$ etc..., but I'm unsure if it is true in general.

Apologies in advanced for the basic question!

Thanks.

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    $\lim (x^2+V)/V = 1$ $\iff$ $\lim x^2/V = 0$ $\iff$ $\lim (x^2-V)/V = -1$. – 2017-01-03
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    @dxiv What's that you say? :) Sorry, have not taken calculus yet. – 2017-01-03
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    `∼` is usually defined in terms of limits, so it helped if you explained what is *your* definition for it. – 2017-01-03
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    If with `~` you mean ‘approximately equal to`, this is *not* a mathematical notion. – 2017-01-03
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    $x^2+V-2V\sim( V-2V)=-V$ . – 2017-01-03
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    Yes. I mean approximately to. – 2017-01-04

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