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

I'm proofreading this in a friend's paper:

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

The same number is singular and it's the thing being compared, so it does seem like is is the right word to use, but then it bothers me that it switches to are in the second half of the sentence. Shouldn't it parallel the first half, as in "There is the same number of elements in the set of odd numbers as there is in the even numbers."? But that sounds wrong.

Note: This is not a duplicate of 'Does “the same number of people” behave as singular or plural?' That question refers to a verb clause modifying "people", and not "the number". Also, I am primarily concerned with the switch to plural in the second half of the sentence, which is not covered in that other question.

Answer

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.