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if $A ⊂ B$, it means that $B$ must have the same but more element that $A$. Recall $A∈B$ read as $B$ is an element of the set $A$. my question is what is the difference between them? for example let B = {1}, $A ={1}$.
clearly$A∈B$, but does $A ⊂ B$? Thank you!

Asaf Karagila
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just walk by
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  • An element of a set is considered different from a singleton (one-element) subset. $1 \in {1,2}$ while ${1} \subset {1, 2}$. – angryavian Mar 21 '22 at 21:50
  • @ angryavian , does that mean that ∈ can only use for element of set and that ⊂ , subset is only for 2 different sets? – just walk by Mar 21 '22 at 21:54
  • for example can i do things like 1⊂{1,2} ? – just walk by Mar 21 '22 at 22:18
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    For first getting used to the notation, it can be helpful to think of numbers like $1,2,3$ etc... as ur-elements, that is... "they are just numbers and are not sets themselves." In such an interpretation you very clearly have $1$ is not a subset of ${1,2}$ because $1$ is not even a set. As you get further along, you'll formally define numbers using sets, so it is good to grow out of this sooner rather than later... but for now that is fine. – JMoravitz Mar 22 '22 at 01:29
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    Do not confuse ${1}$ and $1$. They are not equal. The first is a set containing the number 1 while the other is just the number 1 itself. A lunch box containing a sandwich is not the same thing as a sandwich. You can eat the sandwich. You can eat the contents of the lunch box. You can not eat the lunch box itself. – JMoravitz Mar 22 '22 at 01:31

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