# Creation of a Hamel basis tag

Today I created a new tag: (by the way, it was my first tag creation). I tagged several questions with it, including this one (the one which was the inspiration for doing it). Then, Asaf Karagila posted a comment there saying that he doesn't think that “we need a tag for Hamel bases related questions”. I think we do (although I agree that we don't need a [basis] tag) because there are quite a few questions posted here about Hamel bases.

I would like to know what other MSE users feel about this issue.

• Seems over-specific for its level of use. – rschwieb Feb 13 '18 at 17:31
• Thank you for bringing this to the meta. – Asaf Karagila Feb 13 '18 at 17:34
• Next time, prior to creating a new tag, post here to look for feedback on what other MSE users feel about the potential new tag. – amWhy Feb 13 '18 at 17:42
• @amWhy There is no similarity between this and the creation of a passord tag, since password is not a mathematical concept. But Hamel basis is a mathematical concept. And questions such as asking for a concrete example of a Hamel basis of $\ell^1$ or related to the distinction between a Hamel basis and a Schauder basis are published here. Besides, I cannot imagine a good argument for the existence of the schauder-basis tag which does not apply to the hamel-basistag. – José Carlos Santos Feb 13 '18 at 17:43
• I already removed that comparison. In any case, my point that "quite a few questions" (vague, subjective justification) exist about x, y, z isn't necessarily reason for a new tag. And just because "schauder-basis" exists as a tag, doesn't mean it should, and hence gives no weight to whether hamel-basis should exist as a tag too. I agree with rschwieb; your should-have-first-been-proposed tag is overly specific. – amWhy Feb 13 '18 at 17:48
• @amWhy Is the removal of the comparison supposed to be relevant? I started to write my comment at a moment in which that comparison was present. – José Carlos Santos Feb 13 '18 at 17:50
• My impression is that if the mathematical concept is not sonething people spend at least one chapter in the book to study, then it is not useful as a tag. – user99914 Feb 13 '18 at 17:52
• @rschwieb Can you please explain why you think it is over-specific? I really don't see why someone would think it is more specific than many other tags. – José Carlos Santos Feb 13 '18 at 17:53
• @JohnMa That's an argument that I am sensible to. – José Carlos Santos Feb 13 '18 at 17:54
• @JoséCarlosSantos Yes, I told you I removed it prior to your post/comment because I did not take it to be a valid comparison. I for one, I don't know about you, tend to remove any comment/answer which, upon second thought, isn't/wasn't relevant. I thought I'd comment that I removed it because, just like you thought, I thought there are better comparisons that could be made. Is your comment about the removal of my comparison (and not your comment answering it) supposed to be relevant, anyway? – amWhy Feb 13 '18 at 18:02
• @JoséCarlosSantos I mean, I didn't say tags can't be specific. It's fine to be specific when a particular thing is complicated or has lots of interesting associated questions. It's just mean that it seems relatively rare for such a tag to be appropriate, so being specific doesn't seem to make much sense. – rschwieb Feb 13 '18 at 18:32
• @rschwieb Thank you for clarifying your point of view. – José Carlos Santos Feb 13 '18 at 18:33
• It should be mentioned, I guess, the tag was created before and removed (by me, I think, but Martin can probably say better...) – Asaf Karagila Feb 13 '18 at 18:36
• @AsafKaragila Thank you. I didn't know that. You mean the hamel-basis tag and not the basis tag, right?! – José Carlos Santos Feb 13 '18 at 18:38
• Edeit 5,6 here – user99914 Feb 13 '18 at 18:40

## 1 Answer

This is closer to a comment than to an answer - however, it would be too long to be posted as a comment.

One important thing which might help to judge whether or not the tag can be useful is the intended scope of the tag. Currently the tag-excerpt and tag-wiki simply describe what Hamel basis is. This makes it definitely more specific tag than the previously existing tag that was created and removed several times in the past. For past discussions of this tag see, for example, Can we delete the [basis] tag? and Tag management 2015. For a short period, there was also a tag called basis-dimension.

When I see the tag I can see two ways in which tags might be used. EDIT: As explained in a comment, the OP created tag with the second meaning in mind. I.e., basis in vector spaces (not exclusively infinite-dimensional spaces). I have included this clarification in this post to make it visible a bit better than it would be in a comment.

1. Typically, the distinction between Hamel basis and other types of basis is only needed if we are working in infinite-dimensional spaces. That is also the reason why very often a student does not encounter the name Hamel basis in an introductory linear algebra course - although they are in fact working with Hamel basis. So one possible usage is that this tag is intended for basis in infinite-dimensional vector spaces. I would imagine as typical posts in such tag the ones originally tagged by the OP or questions such as: Can a Hamel basis of $\mathbb R$ over $\mathbb Q$ be measurable? How do I show that infinite-dimensional Banach space has (Hamel) dimension at least $\mathfrak c$?

2. The other possibility is that the word Hamel in the name of tag is used mainly to distinguish this tag from other types of bases, but still includes the finite-dimensional case. So, for example, tag-names such as or could serve basically the same purpose - to make a distinction from base for a topological space, Schauder basis, orthonormal basis, etc. In such case I would imagine here many questions of the type where basis tag was used while it existed. To list a few typical examples: How to find a basis of intersection of two given subspaces of $\mathbb R^4$? How to find a basis of a given subspace with contains the following vectors? How to find basis of kernel and image of this linear transformation?

3. It is also possible that the tag is intended for both types of questions described above. (Well, if we have a separate tag for basis of a vector space, it would probably not be useful to exclude infinite-dimensional spaces.)

I can see some merit to both usages. Still, before discussing this tag further, it would probably good to know which of these (related but still a bit different meaning) was intended by the tag creator.

The tag of the same name was created a removed in the past. (See also Asaf Karagila's comment in chat.) Looking at the questions where the tag was used, it seems that the intention of the user adding the tag was the meaning 1 in the above list. As far as I remember, there has not been discussion on meta explicitly about this tag. (Although the past discussions about might also touched on Hamel basis.)

• That is a very thoughtful reply. What I had in mind was the second option. That is, I believe that the existence of a tag concerning bases of vector space (in the Linear Algebra sense) would be good. It surely seems to me more useful than, say, the ring-isomorphism or the sumset tags. – José Carlos Santos Feb 14 '18 at 13:41
• Thanks for the response - I have added the clarification in my post. (It might be useful for other users who join this discussion to see what were the intentions when the tag was created.) – Martin Sleziak Feb 14 '18 at 13:47