[Tex/LaTex] difference between \bot and \perp, when they are used in exponent

math-moderelation-symbolssymbols

I am used to write $M^\bot$ for the orthogonal complement of the set M. Is this incorrect?

I have seen this question, the answer there says that these two symbols have different spacing. (One of them is treated as relation. Does this difference manifest in some way when the symbols are used at exponent (without any other symbols around them).

I have tried to search a little to find out whether there are other people which use \bot in the same way I do. You can judge for yourself, but I found some occurrences of this.

Here are the same searches with perp instead of bot:

Best Answer

Ah well it all depends.

In the default setup as commented in the linked question they are the same symbol but with different mathclass (so different spacing) \bot is a mathord (like an ordinary letter) and \perp is a relation (like <). Relations get more space either side if used between two symbols but in M^{\perp} the mathlist that forms the superscript only has one atom, so there is no additional spacing applied. That means that M^\bot and M^\perp produce identical output.

You could argue that \bot was better as it is naturally a symbol and a relation is not intended here.

Or you could argue that \perp is better as bot refers to a logical notion of bottom/false whereas perp refers to perpendicular which is somehow semantically related to orthogonal.

Or you could argue that they make identical output so it makes no difference and you can use either.

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