I don't know how to interpret this strange $\prod$

Question

I have got a $\prod$ that is exactly as follows:

$$\prod\limits_{k=0, k \ne k}^n \frac{x-c_k}{c_k-c_k}$$

I am not sure how to interpret this. My guesses are that it equals either $0, or ,1, or ,x$. But perhaps it isn't defined?

Answer 1

dividing by zero is typically frowned upon and I see a zero in the denominator of each factor, unless there is a typo?

Answer 2

Strictly as written the product is $1$. There is no $k$ for which $k \neq k$, the product is thus empty (no $k$ fulfills the condition) and thus $1$.

This seems like some sort of "trick question" or a typo (one of the $k$ should be something else), like $$\prod\limits_{k=0, \kappa \ne k}^n \frac{x-c_{\kappa}}{c_k-c_{\kappa} }$$ which is sort of common in Lagrange Interpolation for instance.