How to say:
"We compute a lower bound on the constant." or "We compute a lower bound for the constant."
"The constant" has been introduced somewhere.
Thanks in advance,
Sasha.
sasha wrote on 11 Aug 2004:
How to say: "We compute a lower bound on the constant." or "We compute a lower bound for the constant."

If you mean by "bound" some kind of minimal value here, it should probably be "for". But if you mean "leap", it should also be "for".

Franke: EFL teacher & medical editor.
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How to say: "We compute a lower bound on the constant." or "We compute a lower bound for the constant." "The constant" has been introduced somewhere.

You will find both in mathematical writing. The latter is probably the more common.

J.
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THANKS EVERYONE.
How to say: "We compute a lower bound on the constant." or "We compute a lower bound for the constant." "The constant" has been introduced somewhere.

The only difference I can see is that a lower bound on the constant is an externally-imposed limitation, whereas a lower bound for the constant is the lowest value it reaches on its own.
The nuance is extremely fine and probably not worth worrying about. And I don't know how widespread my interpretation of the difference is, anyway.

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How to say: "We compute a lower bound on the ... bound for the constant." "The constant" has been introduced somewhere.

The only difference I can see is that a lower bound on the constant is an externally-imposed limitation, whereas a ... fine and probably not worth worrying about. And I don't know how widespread my interpretation of the difference is, anyway.

Neither of those explanations sits easily in my mind with the use of the term "constant". If I compute a lower bond for/on a constant, I'm merely limiting the range within which its (currently unknown but nonetheless invariant) value must fall.
My own preferred usage would be "for", but either works for me.

Cheers - Ian
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How to say: "We compute a lower bound on the constant." or "We compute a lower bound for the constant." "The constant" has been introduced somewhere.

I assume you're estimating a constant. Either is acceptable. Both are widely used. Very widely. Math, mathematically oriented computer science or physics. I don't know about more practically oriented comuter science or engineering or physics type things.
Jon Miller