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Scrolling through the list on tag synonyms on MSE, I found that there were two tags that were suggested to be synonymised with their master tags which were used less than them. Note that both are still pending.

740 questions are tagged whereas its suggested master, , has been used by 281 questions.

The other one (very old) is , used 3630 times, and the suggested master tag has been used 2827 times.

Since they are used more, should we not leave them as they are? For example, an undergraduate may know about Lipschitz continuity, but not of Hölder spaces, so it would be easier for them to search for such questions.

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The question seems (at least in part) to be based on a false premise.

The suggestions are not to merge the tags, but rather to create a synonym. If this was approved then the "minor" tag in the synonym pair could still be used for the purpose of tagging and even searching, but it would be automatically changed into the former.

Thus, somebody wishing to use the "minor" name could still do this, and the system then would automatically map this to the "major" name. A case you describe, a common notion is subsumed by a less common one, is exactly a use-case for a tag synonym.

For further details see What are tag synonyms and merged tags? How do they work?

The merging of tags is a related but separate process. Only moderators can do this. Here, the "minor" tag can in fact disappear, but it is also possible to keep the "minor" tag as a forward.

In specific cases you mentioned, the idea is certainly to keep the "minor" tags, and thus the concern you have does not really arise.

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