Term for "lower numeric bound" - analogous to “capped”

What term should be used for describing limiting the lower range of a number?

We (often) use "capped" to refer to a limit on the upper value of a range.

What is the analogous term for limiting the lower end of the range?

More:

I want a past tense word that means "a hard lower limit has been placed (on something)".

In the same way that we might say "Your medical costs have been capped at \$5000" (that's the most you will pay), I seek a word where I can say "Your medical costs have been XXXXed at \$200" (that's the least you will pay).

It's not euphonious, and moreover colloquial, but floored is used in this context. More standard, but with a mathematical flavor, is bounded below.

• This is just a repeat of the first answer to the question by jbeldock
– user10893
Commented Jun 27, 2013 at 7:45
• @simchona, I don't think jbeldock used floored as a verb in its own right, only as a noun. Commented Jun 27, 2013 at 7:46
• I'm going with "floored". I am a programmer and "floor" is a function that returns the next lowest integer, but would be understood in context: "the monthly cost has been floored at \$10." Commented Jun 27, 2013 at 8:41
• Although it may be understood in certain technical areas, the use of "floored" in this way would (I think) seem very strange in British English - and may indeed need explanation. What's wrong with "set at a minimum of"? Commented Jun 27, 2013 at 10:39

The Engineers I work with refer to the noun as "the floor," or the "lower bound." I do not believe there is an analogous single word to "capped," but you can certainly say, if somewhat less euphoniously than otherwise desirable, "lower bounded," or "always exceeds," or if speaking to a mathematician "is bounded below by."

There are many ways to say this, though I can't think of one which is exactly what you're asking for. Precisely what you use will depend a lot on your context and your audience.

You might say exceeds:

The projected average temperature definitely exceeds the average of the previous thirty years.

You could also say at least:

We estimate a production rate of at least 3 units per hour.

But in some contexts, simply saying has a lower bound sounds much better:

The function has a lower-bound of 2x.

You might also consider a minimum of or at (a) minimum:

You will need to pay a minimum of \$200 for your medical costs.
Your medical costs will be \$200 at a minimum.

• Those meanings aren't what I'm getting at. I want a past tense word that means "a hard lower limit has been placed (on something)". In the same way that we might say "Your medical costs have been capped at \$5000" (that's the most you will pay). I'm looking for a word where I can say "Your medical costs have been XXXXed at \$200" (that's the least you will pay). Commented Jun 27, 2013 at 4:53
• @Bohemian: Andrew has suggested floored as the only term that seems to come close to satisfying your requirements - you could try checking online to see how common the usage is. I admit that I've only come up with a single Google hit at my first attempt: Medical expenses were floored at 5% back then - which hardly licenses the use of this term. Commented Jun 27, 2013 at 8:20
• Google returns for "were floored at" -"were floored at the" include following 5 relevant hits within the first 100 hits (mostly meaning 'we were blown away by...'): the steers were "floored" at \$3 a pound; Small Area FMRs were floored at 80% of the metropolitan FMR; Signal Values were floored at 100; maine heifers were floored at 700; Steers were floored at a minimum \$2 per pound; Commented Jun 27, 2013 at 8:32

Might be worth thinking for a minute about what the term means wrt real world objects that are "capped", i.e. putting a cap on a physical object.

What is at the other end of that object? A beer-mat! A colleague of mine likes to use "Cupped", which works if you think of what your hands do when holding something vertically, but I have never seen this term used anywhere else though.

The real world object also has a "Base" so maybe "Based" would be nice NEW term to start using?

There is no term (for the past tense of floor as a verb) because there is no logical need for it. Capped implies that action has been taken to present any rise. In the use case you describe, you are simply imposing a minimum.

That situation is made clear by the sentence Your medical costs will always exceed \$200.

If your example was framed in terms of a minimum return (rather than a cost) then there could be justification for a term describing active intervention. Even then, the idea is well expressed by Notwithstanding any periods without tenants, your minimum rental earnings are guaranteed at \$10000 per year.

• 'That situation is made clear by the sentence: Your medical costs will always exceed \$200' does not clearly illustrate 'imposing a minimum' - it may well be just mentioning what is always found to be true. There are, however, actually imposed lower bounds - for instance, minimum speed limits on some roads. And I don't see any evidence provided to show the non-admissibility of the stated use of floored (though admittedly Andrew Lazarus doesn't provide evidence showing its use either). Commented Jun 27, 2013 at 8:17
• @Fortiter Floored is very commonly used in finance. For example, "the interest rate is capped at 5% and floored at 3%".
– user24964
Commented Jun 27, 2013 at 8:44
• If there weren't a need for such a term, people wouldn't be using "floored" for it. Commented Jun 27, 2013 at 12:10
• People use 'insegrevious'. Commented Jun 27, 2013 at 22:28