Is it a good idea to combine the glossary and the list of notations in a mathematical PhD thesis?

I am considering including a glossary and a list of notations in my PhD thesis on mathematics. Is it a good idea to write them separately or combine them?

For example, a typical entry of the list of notation is:

[a,b] The commutator of a and b, defined by [a,b]=a^{-1}b^{-1}ab.

An entry of the glossary is:

Commutator The commutator of a and b is defined to be the product a^{-1}b^{-1}ab.

(Note: the definition of commutator is well-known to mathematicians, but since another definition aba^{-1}b^{-1} is also possible, I would like to add the definition to avoid any possible ambiguity.)

I have a strong feeling of combining these two entries together, maybe even combining the glossary and the list of notations together.

Is it a good idea to combine the glossary and the list of notations in a mathematical PhD thesis?