What is the notation for the statement for some integer n ?

[Nothing000]

What is the notation for the statement "for some integer n"?

What is the notation for the statement "for some integer n"?
Is it $$\forall n | n \in Z$$
Or is it $$\{n | n \in Z \}$$

Or is it something else?

$$|$$ does mean "such that", doesn't it?

 

[Office_Shredder]

The first notation you show means for all integers n. The second is the set of all integers. What you're looking for, I think, is notation that indicates there exists at least one n that the statement is true for. I don't know how to make the symbol in latex, but it looks like a backwards capital E. Pretending my E is actually backwards for the purposes of this:

Example:

E n s.t.$$\sqrt{9} = n$$

could be read as there exists n such that the square root of 9 equals n. Alternatively, you could say the square root of 9 equals n for some n

 

[Nothing000]

What is the symbol for "such that"?

 

[Nothing000]

Tell me if I am interpreting my first two notations correctly.
I would read $$\forall n | n \in Z$$ as "for all n such that n is an element of the set of integers".

And I would read $$\{n | n \in Z \}$$ as "the set of n such that n is an element of the set of integers".

 

[Office_Shredder]

First, I found how to do the symbol:

$$\exists n \in Q s.t. n \in Z$$

reads there exists n a rational such that n is an integer (a trivial statement, I admit :) ).

generally, the vertical bar is only used in your second example, for your first example it would be better to put s.t. (for such that).

 

[Nothing000]

$$\exists n \in Q s.t. n \in Z$$

reads there exists n a rational such that n is an integer

What do you mean "there exists n a rational"?

 

[Nothing000]

Off the topic, but do you know what the RMS voltage is of a triangle wave?

 

[HallsofIvy]

What do you mean "there exists n a rational"?

Better grammar: there exist a rationa number n such that n is an integer.

 

[Nothing000]

Better grammar: there exist a rationa number n such that n is an integer.

That makes more sense. Thanks.