[Math] Learning math symbols

elementary-set-theorylinear algebranotationquantifiers

I am taking linear algebra and none of this stuff is expained. I found this helpful link http://www.math.ucla.edu/~pskoufra/M115A-Notation.pdf

but it is missing a lot of what I need to know. Just right now though what does v and ^ mean in the context of linear algebra and set stuff? It is not defined anywhere in my book and it is exceptionally frustrating trying to read this…stuff. Also what does something like upside down A$ x(x \epsilon A _> x \epsilon B)$ mean?

More context

$ x(x \epsilon A _> x \epsilon B) $^ 4 \exists x \in B $ ^ $x $ \not\in A)$

Best Answer

Wikipedia has a list of logic symbols. The expression:

$\forall x ~ [(x \in A \implies x \in B) ~~~\land~~~ (\exists x \in B ~\text{ s.t. }~ x \in A)]$

can be interpreted to mean:

For all $x$, both of the following claims hold true:

  • If $x$ is in $A$, then we also know that $x$ is in $B$.
  • There exists some $x$ in $B$ such that $x$ is also in $A$.
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