The use of conjunction "and" to avoid repetition

Question

I apologize if my question seems trivial for people who study literature and English language in depth.

My question is basically related to the following statements:

1. The existence of X
2. The convergence of X to Y

Here, X and Y are nouns. So I would like to ask the following questions:

1. Assuming I combine statement 1 and statement 2, when I write "The existence of X and the convergence of X to Y" seems to be redundant. So, is this grammatically correct?
2. Now, if I reduce repeated words to obtain "The existence and the convergence of X to Y", does it automatically mean X satisfies both statement 1 and statement 2 in general English language?

I apologize if my question is out of context or the way I phrase my question to be strange since I come from mathematical background and English is not my native language.

Thank you very much! Any comment is much appreciated!

Answer 1

The short answer is only if the existence of Y is also established. When you link two nouns with a conjunction like this, they both apply to what follows.