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Does "full" and "empty" always mean "completely" full and empty?

Isn't it ambiguous to say:

The variable X represent the weight of the container when it is full.

when we are talking about the weight of the container that is full to the brim.

I think it has to be like

The variable X represent the weight of the container when it is completely full.

Do the two adjectives on their own mean "completely full" and "completely empty" and we should use a modifier only when we want to talk about the state of not being completely full or empty:

The variable X represent the weight of the container when it is not completely full.

Or maybe it's always better to use a descriptive or an intensifier adjective?

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    Say you're loading bicycles into a container. Is the container full when you can't fit another bicycle inside? You mention some kinda brim (dunno if you're being literal or not) – can you keep piling these bicycles on top of each other, or do you stop at the brim? Could you expand a little more on the context in which this is used? Is this math or programming or what? – user3395 Sep 6 '19 at 0:03
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    It should be the variable X represents. And unless you qualify the word, it's assumed that it means completely in the positive sense. It's sufficient to say I'm sorry the bus is full; you don't need to say I'm sorry the bus is completely full. However, it can't hurt to add completely to the negative sense. (In the same example of the bus, it might not be apparent to somebody looking from the front of the bus that there's a single seat still available.) On the other hand, it would be pretty obvious if every seat were empty except for one. – Jason Bassford Sep 6 '19 at 0:22
  • @userr2684291 Yes, it is a mathematical thing, basically an explanation for the notation X. – Cardinal Sep 8 '19 at 20:32
  • @Cardinal I think in such a context you don't have to make clear whether something is full or "conventionally full" (math deals with "absolutes", and when hypothetical or "pure" situations are presented, you're essentially redefining full, or defining it for your context). Except, why do you need variables to represent that? Do containers change in size? But anyway, if you give more context we might know better. The answer you accepted talks about actual English, so that's more beneficial for learners, but depending on the context, completely might be superfluous where you want it. – user3395 Sep 9 '19 at 12:49
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    @Cardinal That boolean sense is exactly what I meant when I was talking about "absolute" concepts in math. You can without a worry in the world say Let X represent the weight of a/the full container, and Y the weight an/the empty container. Because there is no real wiggle room, or real-world details, you've successfully defined states full and empty. Even if you now talk about some other variable approaching X or whatever, it's obvious that full means "completely full", or that that aspect/nuance doesn't matter at all. – user3395 Sep 9 '19 at 14:50
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"Empty" and "full" in US English mean all the way one way or the other but do not necessarily mean "completely" empty or full. For example, I take a glass of water. I turn it over so the water pours out. I now call it "empty" even though a few drops of water might still remain inside.

If I fill a cup of water at a restaurant, I call it "full" even though there is a little room in the glass for more water. If I filled it to the rim, it couldn't be carried or lifted without possibly spilling. But it's full, that is, it's as full as it should be.

Where absolute exactness is required, we use more words to specify the precise situation.

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