Writing propositions symbolically

[brookey86]

Homework Statement

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.

Homework Equations

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 ∃ F_k+1(k) … F_k+k(k).

 

[Char. Limit]

Homework Statement

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.

Homework Equations

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 ∃ F_k+1(k) … F_k+k(k).

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 F_k+a(k) means.