I am confused. Please, help me!
I am studying "Set Theory" and I am really not trusting in the quality of the material provided and since I am not a math expert I decided to ask in order to clear any doubts lest I learn something the wrong way.
Are the symbols below REALLY used in set theory:
Above is an IMAGE to make sure you are seeing the same thing as I am (I know fonts may be decoded incorrectly).
Thank you very much!
Best Answer
As the comments have said, no, the symbols you're seeing are not the actual symbols - there's clearly been an encoding error.
For the record, the correct symbols are as follows:
The emptyset is "$\emptyset$" ($\LaTeX$ code
\emptyset).The elementhood relation is "$\in$" ($\LaTeX$ code
\in).There is a bit of ambiguity around the "contained in" (or "subset of") relation. We basically have three relevant symbols: "$\subseteq$" ($\LaTeX$ code "
\subseteq), "$\subset$" ($\LaTeX$ code\subset), and "$\subsetneq$" ($\LaTeX$ code\subsetneq). Generally the first is most common and refers to subsethood broadly, while the third refers exclusively to proper subsethood. The second is annoying: usually it refers to proper subsethood, but occasionally it's used for the broader notion of subsethood in general (Munrkes' topology book does this). My experience is that $\subset$ is largely avoided in more modern literature.The same ambiguity exists with respect to the "contains" (or "superset of") relation, the relevant symbols being "$\supseteq$" ($\LaTeX$ code
\supseteq), "$\supset$" ($\LaTeX$ code\supset), and "$\supsetneq$" ($\LaTeX$ code\supsetneq).The negation of a relation ("not an element of," "not a subset of," etc.) is gotten by putting a line through the relation itself, e.g. "$\not\in$" or "$\not\subseteq$" ($\LaTeX$ code
\not\[command]).Intersection and union are "$\cup$" and "$\cap$" ($\LaTeX$ codes
\cupand\cap) respectively.Incidentally, if there's a symbol whose $\LaTeX$ code you don't know, try detexify.