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The statements are not the same. In statement 1, one single d holds for all a; in statement 2, different a may be associated with different d. Statement 2 only says that there exists at least one d for each a.
This distinction is the difference between continuity and uniform continuity. Let I be a real interval and ƒ a real-valued function on I. Then:
(i) ƒ is continuous on I iff
(ii) ƒ is uniformly continuous on I iff
The two definitions are different. In (i) δ depends on x; different δ may need to be chosen for different x. In (ii), one single δ has to work for all x.
Since Statement 2 doesn't say "there exists a unique d", I would interpret this in the same manner as for Statement 1; namely, that there exists some element d for each a. The element d doesn't have to be unique (a different d for each a).
I'm trying to understand what happens when quantifiers in the prediate are swapped.