Learning math symbols

Question

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)$

Answer 1

Sometimes, $\wedge$ is used to mean "and", whereas $\vee$ is used to mean "or." The LaTeX code for these are \wedge and \vee, respectively.

$\forall$ means "for all". So if you wrote $\forall x \in S$, this means literally "for every element $x$ in the set $S$."

$\exists$ means "there exists". This is commonly used with $\forall$ in mathematics. For instance:

Let $E$ denote all even positive integers. Then, $\forall x \in E$, $\exists n \ge 1$ such that $2n = x$.

This means that for any element in the set $E$, we can find some number $n$ greater than or equal to 1 that, when multiplied by 2, becomes $x$. In other words, all even numbers are multiples of 2.

This is a trivially easy example, but the compactness of this nomenclature is certainly useful when you start getting into more complicated definitions of ideas.

Answer 2

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 $A$.