Consistency of "There is the same number of elements in... as there are in..."

Solution 1:

Either you are comparing one thing with another single thing, in which case they should both be 'is', or you are comparing one set of things with another set of things, in which case they should both be 'are'; you shouldn't mix and match.

Whether you consider 'the number of elements in a set' to be a single unit (a Number, which describes a characteristic of the set of odd numbers) or a multiple unit (all the odd numbers, and we are counting them) is more a matter of personal preference.

However, the set should be described the same way in both halves of the sentence:

There is the same number of elements in the set of even numbers as there is in the set of odd numbers.

or

There are the same number of elements in the set of even numbers as there are in the set of odd numbers.

Or, you could suggest a rewrite along the lines of

The set of even numbers has the same number of elements as the set of odd numbers.

Solution 2:

If we rewrite the sentence to:

"There is the same count of elements in the set of odd numbers as there is in the even numbers."

... it sounds less awkward, and also gives us a clue. In this sentence, the verbs ought to match, and probably ought to be "is". However, it'd also be better to rewrite the sentence to be less awkward.

Perhaps: "The set of even numbers has the same number of elements as the set of odd numbers."