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I am not sure if the word value is countable or non-countable. So I am not sure if i should add an article before it in a context like:

Our method adds a value over their method.

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Value is countable in some contexts, but not here. The relevant meaning of value from Merriam-Webster is

3: relative worth, utility, or importance

a good value at the price

the value of base stealing in baseball

had nothing of value to say

"Relative worth, utility, or importance" is not something that's countable.

If you were talking about a different sense of value, like "a numerical quantity", then you'd have a countable noun. For example: "One possible value of X is 20".

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