Is a $\Omega$-Spectrum a connective one? I can't find this result anywhere, but it seems pretty straightforward. I want to avoid silly mistakes, but I can't see any fault. I'd love to receive some feedback
Let $X$ be a $\Omega$-spectrum (of compactly generated topological spaces). By definition for $q<0$, $$\pi_q(X)=\lim_k \pi_{k+q <k}X_k$$
But since $\pi_i(X_k)\cong \pi_{i}(\Omega X_{k+1})\cong \pi_{i+1}(X_{k+1})$ the spaces are more and connected, in particular, $X_k$ is $k-1$-connected and therefore $\pi_q(X)=0$.
Is that correct?

Direct answers would be helpful. I believe you are saying for connective $\Omega$-spectrum $X$, $\pi_i(X)=0$ for all $i\leq -1$. For non connective $\Omega$-spectrum, there are nontrivial negative homotopy groups.
