Thread: 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

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:



I believe this has the same meaning:

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:



I believe this has the same meaning:

does ":" mean such that?

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

Originally Posted by Noxide

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.

if and only if

Edit: upon reflection, what I wrote above:

Originally Posted by undefined

I believe this has the same meaning:

isn't precise enough, because 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 symbol, like I did in this post.