Considering the following two sentences, is there a difference between them? If so, do "all possible" and "any" make the difference?

Note, serializable and serial schedules are two different types of schedules in distributed database systems. However, the word "equivalent" here means that they give the same results when executing a set of transactions. For example, given that a is a serializable schedule and b is serial. They are equivalent if they execute the same set of transactions and give the same results.

  • "A serializable schedule ensures that the execution of n transactions is equivalent to all possible serial schedules of the same n transactions."
  • "Formally, a schedule S of n transactions is serializable if it is equivalent to any serial schedule of the same n transactions"

In other words, can I say that the meaning of the former sentence is different than the latter one?



1 Answer 1


Ok first of all, using a different example, there can be a clear difference between "any" and "all" in certain contexts:

My son will eat any of the cakes.

My son will eat all of the cakes.

In this example both imply that there is a limited selection of cakes on offer because it says "the cakes". Using "any" means that all of the cakes are an option, and that the son can select and eat a cake from all those on offer; whereas the second using "all" implies that he will eat every single one of them himself. In this context where there is a limited scope, the two have completely different meanings.

Thing is, in your example it isn't simply the difference between "any" and "all":

..is equivalent to all possible serial schedules..

..is equivalent to any serial schedule..

It is actually the difference between "any" and "all possible".

I don't fully understand the subject in your examples so let me use another one:

The app works with any model of smartphone

The app works with all possible models of smartphone

In this example, the first using "any" implies that it is a universally compatible app. A scope has not been set as it was in the cake example where it implied a limited selection of cakes. It doesn't say "any smartphone currently on the market". So this implies, rightly or wrongly, that the app will work on future smartphones too - literally any phone.

Saying "all" smartphones doesn't strictly define a scope either, but the word "all" does imply a countable number, so arguably this does not cover phones that could be made in the future. However, saying "all possible" smartphones completely removes any possible limitation. It implies that any smartphone that could possibly emerge in the future would work with this app as well.

So no, there is no clear difference in your two examples, because of the inclusion of the word "possible". "Any" does not define a limited scope, and "all possible" removes any inference of one.

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