Thank you for giving me feedback about how my question was ambiguous. Sorry for the confusion, and I reformulated my question.
Reformulation: Let's say a black box is giving me a real number every second in a truly random way.
By truly random, I mean that there is no way for one to predict what number will come next.
But I don't yet know if the black box is giving me numbers in a random way or in some way with a pattern.
Is there any way for me to prove that the black box is giving me numbers in a truly random way?