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I want to say that "the value decreases at a rate at least x" (i.e. faster than or equal to x). Does the phrase "the value decreases at minimum rate x" mean the same thing? If not, is there any other way to rephrase it?

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Although not suitable in all contexts dv/dt<=-x is unambigous –  Taemyr Jan 10 at 13:37

2 Answers 2

Minimum means at least, so "the value decreases at minimum rate x" can mean what you want. However, I'd advise against it, since it could also be understood to say "the value decreases at the minimum rate, which is x", i.e. that it never decreases any slower or faster than x.

Therefore, I suggest:

The minimum rate at which the value decreases is x.

This unequivocably means that the rate of decrease is at least x, but possibly more.

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Another option is "the value decreases at a minimum rate of x", which implies that there may be other rates at which the value decreases other than x (the minimum rate). –  ogicu8abruok Dec 9 '13 at 17:17

An undesired interpretation is likely to occur for "The value decreases at minimum rate x": "The value decreases as slowly as it can, which is rate x". I'd avoid the word minimum and instead say, "The value decreases at a rate no less than x".

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Avoiding the word minimum isn't necessary if you say the minimum rate at which the value decreases is x. –  Daniel Jul 19 '12 at 22:00

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