I'd like to state that when a variable is between say $1$ and $2$, certain properties hold. Since this is a physical variable, the limits aren't precise. Is it acceptable to write: $$2 \gtrsim x \gtrsim 1$$ Although this seems like that intuitive symbol to use, I haven't seen it used anywhere.

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Oh i see, "smaller than about" 2 and "greater than about" 1, a good question. +1, I don't see what the problem would be with writing it like that, although some may have reservations about it. There might be better nomenclature, however, I like your way of writing it. – Rustyn Feb 9 '13 at 21:44

Sure, that's a fine symbol to use, as long as you explain what you intend it to mean.

For example, you could write

If the quantity $x$ satisfies $$2\gtrsim x\gtrsim 1$$ (where this notation indicates _____ ), then ...

or

Let the notation $x \gtrsim y$ indicate _____ . Then when the quantity $x$ satisfies $$2\gtrsim x\gtrsim 1,$$ ...

You could also use error bounds, e.g. $2\pm 0.1$, if you have such information regarding the imprecision you want to specify.

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Isn't that equivalent to saying the notation really isn't used by anybody? If so, is there a better way to write this? – nbubis Feb 9 '13 at 21:48
Almost any time the question "Can I write property / relation $x$ as ..." is asked, this is the answer, unless there is already a notation for it. +1 – Arthur Feb 9 '13 at 21:49
@nbubis: No, it is not equivalent. Honestly I have no idea what the standard notation is, but your choice of symbol is not confusing (e.g., it would be inadvisable to use "$=$" to mean "greater than about"), so it is fine. – Zev Chonoles Feb 9 '13 at 21:52