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⊂ and ⊃ symbols

Some authors use the symbols ⊂ and ⊃ to indicate subset and superset respectively; that is, with the same meaning and instead of the symbols, ⊆ and ⊇

Other authors prefer to use the symbols ⊂ and ⊃ to indicate proper (also called strict) subset and proper superset respectively; that is, with the same meaning and instead of the symbols, ⊊ and ⊋.

https://en.wikipedia.org/wiki/Subset

Whether we should use ⊂ or ⊊ to represent the proper (strict) subset? Which symbol have more use?

(Folks, most of the time I work with languages. I'm not a mathematician at all. Just in case.)

Arctic Char
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john c. j.
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    As Wikipedia says, some authors use one and some use the other. Both are quite common. – Eric Wofsey Oct 25 '20 at 21:34
  • Cf. this question – J. W. Tanner Oct 25 '20 at 21:39
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    I like using $\subset$ for subset or equal. I find that I rarely need to talk about proper subsets. You can use whatever you want as long as you make it clear to the reader what you mean. – morrowmh Oct 25 '20 at 21:45
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    To be absolutely clear, can use $\subseteq$ to mean proper/equal subset and $\subsetneq$ to mean proper subset and never use $\subset$. No ambiguity. But different authors will do different things. If I see $\subset$ with no indication what which meaning they are using and no context indicating it must be a proper subset, I would assume is proper or equal. ... If I were dictator of the world I would declare $\subset$ and $\subseteq$ are exactly the same and authors can use either for style and/or emphasis. And must use $\subsetneq$ for proper. But I'm not dictator of the world. – fleablood Oct 25 '20 at 21:57
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    I strongly recommend that you not use $\subset$ at all, precisely because in current usage it is ambiguous. Use $\subseteq$ and, for proper inclusion, either $\subsetneq$ or $\subsetneqq$. – Brian M. Scott Oct 25 '20 at 22:03
  • Exactly what @MichaelMorrow said, plus that it does not matter which convention is more popular, but it matters most that your reader knows exactly what you mean. – user21820 Oct 27 '20 at 15:52

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