# Writing propositions symbolically

1. Sep 14, 2011

### brookey86

1. The problem statement, all variables and given/known data

For each positive int k, there are k consecutive pos ints that aren't perfect-squares.

I'm trying to write this in symbolic logic, but am getting messed in the second part and might be a little off on the first.

2. Relevant equations

3. The attempt at a solution

∀ k > 0 - For each positive int k

F(k) indicates that k is a not a perfect square. (can this be written symbolically instead?)

∀ k > 0 ∃ Fk+1(k) … Fk+k(k).

2. Sep 14, 2011

### Char. Limit

If you want to write that symbolically, you could write something like this:

$$F(k) \leftrightarrow k \neq n^2, n \in \mathbb{Z}$$

Of course, you'd still have to define what Fk+a(k) means.