Can I add this assumption for arbitrary family?

Question

Perhaps, my question is straightforward but I want to make sure. let's consider, $\mathcal F=\{f_{\xi}\colon \xi<\mathfrak c\}$ family of functions from $\mathbb R\to\mathbb R$. If want to prove something by using the family $\mathcal F$. Can I assume each function in $\mathcal F$ repeated continuum many times even though does not state in the theorem? $\mathcal F$ just contains a continuum many times.