The 'one hand' could be any generic hand (no article) or a specific one (definite article). 'The other' refers to the 'matching hand' of the first one. There can only ever be one, and it is being referred to explicitly as the partner of the first, therefore it needs a definite article.

Understanding the Context

Both 'a single' and 'one single' are correct and commonly used phrases in English. They are interchangeable and can be used to emphasize the singularity of an item or person. The difference is that "one" puts more emphasis on the number such as I have 4 computers and a printer/I have 4 computers and only one printer. So when you say a feature of my work or one feature of my work, it means the same, with the only difference that "one" is emphatic compared to "a".

Key Insights

One-to-one is used when you talk about transfer or communications. You may use one-to-one when you can identify a source and a destination. For eg., a one-to-one email is one sent from a single person to another, i.e., no ccs or bccs. In maths, a one-to-one mapping maps one element of a set to a unique element in a target set. One-on-one is the correct adjective in your example.

Final Thoughts

See Free ... Which one is grammatically correct or better? I have two assignments, One of them is done. I have two assignments, One of which is done. I watched a video tutorial that the teacher said the ... pronouns - "One of them" vs.

"One of which" - English Language Learners ... 0 The phrase 'one of the' is used to describe something/someone from the same group. There are many birds on the tree. One of the birds is red.