What does the expression "generally" mean in mathematics?

Question

Mathematics

For example in logic/set theory.
I couldn't find a definition.
Here I have an example.
Given:
set of numbers X: 1; 2; 3; 4.
set number Y: 1; 2; 700; 800.
Is the following statement #1 true:
In general, element X is not equal to element Y.
And is the following statement #2 true:
In general, element X is equal to element Y.
Thank you.

Answer 1

It's elementary.
If, considering a certain situation, we introduce some boundary conditions, this is a special case.
If there are no boundary conditions - general.
The correctness of any statement in a particular case does not mean its correctness in general.
Loyalty in the general case covers all private.
In your question, both statements are false, since the element X can be either equal or not equal to the element Y. If it is easier for you to understand, consider each statement from the point of view of "is there at least one violation of it?". Loyalty generally means that there are no violations.