Complexity arises with...

[nyggus]

1. The complexity of a problem arises when a value of the parameter a is large.
2. The complexity of a problem increases with an increasing value of the parameter a.

Which one is better/correct? I would prefer the second meaning (as the two sentences have slightly different meaning IMO) but am not sure whether it is a correct sentence or not.

Thanks,
Nyggus

[MikeNewYork]

1. The complexity of a problem arises when a value of the parameter a is large.
2. The complexity of a problem increases with an increasing value of the parameter a.

Which one is better/correct? I would prefer the second meaning (as the two sentences have slightly different meaning IMO) but am not sure whether it is a correct sentence or not.

Thanks,
Nyggus

I like 2 better. I would just eliminate "the" before "parameter" if "parameter a" is the name of something.

[nyggus]

I like 2 better. I would just eliminate "the" before "parameter" if "parameter a" is the name of something.

Thanks, MikeNewYork. The "a" is the symbol of a parameter considered, and if it has been introduced earlier, "the" should be there, I think -- shouldn't it?

Best,
Nyggus

[MikeNewYork]

Thanks, MikeNewYork. The "a" is the symbol of a parameter considered, and if it has been introduced earlier, "the" should be there, I think -- shouldn't it?

Best,
Nyggus

Here we go (again) with articles. If the word "parameter" is used, the article is needed. But if "parameter a" is the name of a parameter, then no article is used.

[nyggus]

Here we go (again) with articles. If the word "parameter" is used, the article is needed. But if "parameter a" is the name of a parameter, then no article is used.

Indeed, here we go again. I am not sure "parameter a" is the name of a parameter; "a" is the name of a parameter. Should we really use no article? I must say I am really confused here. Some time ago a friend of mine told me one should not use an article in such a situation, but when we searched for it in many jounals we found that the article was usually used.

Best,
Nyggus

[BobK]

Indeed, here we go again. I am not sure "parameter a" is the name of a parameter; "a" is the name of a parameter. Should we really use no article? I must say I am really confused here. Some time ago a friend of mine told me one should not use an article in such a situation, but when we searched for it in many jounals we found that the article was usually used.

Best,
Nyggus

Would it be clearer if we avoided "a" and said "the value of the X parameter"? - calling it "a" hurts my brain, because "a" can be an article.

The complexity of a problem rises when the value of the X parameter is large.
This sentence is talking about any instance of a problem that involves the X parameter; a large value for that parameter makes the complexity of such a problem rise.

One could also say

The complexity of a problem rises when the value of the parameter X is large.

But when talking about a particular problem, where the X parameter has a certain value,

The complexity of the problem rises because the value of parameter X is large.

I think the articles you've seen are referring to particular problems.

b

[nyggus]

Thanks, BobK. And practice you brain because many parameters in mathematics has a symbol "a", and avoiding it would be just confusing for those who know the parameter.

Best,
Nyggus