# Notation

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• Jun 4th 2010, 11:53 AM
Noxide
Notation
I am trying to say: Every a in A is in B

Is the following notation correct?

[(universal quantifier) a (epsilon) A] (epsilon) B
• Jun 4th 2010, 12:05 PM
undefined
Quote:

Originally Posted by Noxide
I am trying to say: Every a in A is in B

Is the following notation correct?

[(universal quantifier) a (epsilon) A] (epsilon) B

I could be wrong but I think what you wrote would not be considered correct use of notation.

I would instead write:

$\forall\ a \in A: a \in B$

I believe this has the same meaning:

$a \in A \Longrightarrow a \in B$
• Jun 4th 2010, 12:24 PM
Noxide
Quote:

Originally Posted by undefined
I could be wrong but I think what you wrote would not be considered correct use of notation.

I would instead write:

$\forall\ a \in A: a \in B$

I believe this has the same meaning:

$a \in A \Longrightarrow a \in B$

$\forall\ a \in A: a \in B$

does ":" mean such that?

If you're interested I'm just talking about the case where A is a subset of B
• Jun 4th 2010, 12:36 PM
undefined
Quote:

Originally Posted by Noxide
$\forall\ a \in A: a \in B$

does ":" mean such that?

If you're interested I'm just talking about the case where A is a subset of B

You could read ":" aloud by simply pausing: "For all a in A, a in B." Or you could read it as "it is true that."

Here's another way.

$A \subseteq B$ if and only if $\forall x(x\in A \Rightarrow x\in B)$

Edit: upon reflection, what I wrote above:

Quote:

Originally Posted by undefined
I believe this has the same meaning:

$a \in A \Longrightarrow a \in B$

isn't precise enough, because $a$ is unspecified, thus the expression is not a sentence/proposition in the language (it cannot be assigned a truth value); we would still need the $\forall$ symbol, like I did in this post.