What does the symbol described below mean?

The symbol kind of looks like this: ε, but it's more like a sideways u with a line through the middle.

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Perhaps set membership. Sea also Wikipedia's list of math symbols. The notation dates back to Peano according to Jeff Miller's Earliest Uses of Symbols of Set Theory and Logic: Giuseppe Peano (1858-1932) used an epsilon for membership in Arithmetices prinicipia nova methodo exposita, Turin 1889 (page vi, x). He stated that the symbol was an abbreviation for est; the entire work is in Latin. –  Bill Dubuque Nov 10 '12 at 1:46
Peano also used a backwards epsilon for "such that" in 1898, see this prior question. –  Bill Dubuque Nov 10 '12 at 1:53
sideways u ... pointing which direction? Line through the middle: vertical, horizontal, diagonal? –  GEdgar Nov 10 '12 at 1:55
@BillDubuque I know Peano came up with $\forall$, $\exists$, $\nexists$, etc. but I did not know he also invented $\ni$ for "such that". –  glebovg Nov 10 '12 at 1:56
@ncmathsadist Surely $\in$ is one possible interpretation of the OP's description "looks like this: ε, but it's more like a sideways u with a line through the middle." –  Bill Dubuque Nov 10 '12 at 1:59

Do you mean $\in$? This means "an element of". For example, if we denote the set of natural numbers by ${\mathbb N}$ then $1 \in {\mathbb N}$. Similarly, $1,2,3, \ldots \in {\mathbb N}$, and $- 1 \notin {\mathbb N}$. Sometimes you might also see $\ni$, which some authors use for "such that". You might also be referring to $\epsilon$, which is the same as $\varepsilon$, or perhaps you mean $\not\subset$, which usually means "not a subset of".

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Interestingly, I've seen $\ni$ where the an element of a set is to the right of the set, like $\supset$ is used for set membership. –  amWhy Nov 10 '12 at 1:52
You can use $a \in X$ or $X \ni a$, they mean the same (at least to all the books I've seen this in. But of course it's always better to just mention what you mean by a notation before using it. –  Patrick Da Silva Nov 10 '12 at 1:58
@PatrickDaSilva I have not seen people use $\ni$ for membership. It makes more sense to use $\in$ because it looks like the letter e for element. It also looks like $\epsilon$, again epsilon (the first letter is e) for element. –  glebovg Nov 10 '12 at 1:59
Actually I never see people using $\epsilon$ to denote membership. I know that the symbol $\in$ is essentially an epsilon but I reserve $\varepsilon$ for numbers and $\in$ for membership, this thing $\epsilon$, I hate it. –  Patrick Da Silva Nov 10 '12 at 3:06
This is the Greek letter $\epsilon$, but the font is a little different like this $\varepsilon$.
@Jennifer It's called epsilon: $\epsilon$, which can be formatted on this site using $\epsilon$ –  amWhy Nov 10 '12 at 1:55
Its variant is \varepsilon. –  ncmathsadist Nov 10 '12 at 1:57