According to wikipedia,
"...the Weierstrass factorization theorem in complex analysis, named after Karl Weierstrass, asserts that entire functions can be represented by a product involving their zeroes."
Yet the exponential function is an entire function with no zeros, is there a implicit stipulation in this theorem that entire functions must have at least one zero in order for the theorem to apply?
Note: Maybe this is stupidly obvious, but I wan't to make sure there isn't a more advanced point of view which resolves this by considering points whose real part approaches negative infinity, or something of the like.