Assuming your claim is not equivalent to "matrix multiplication is in O(n^2)", then it is false assuming conventional mathematics (i.e. uncountable sets exist), because j in R is uncountable, and algorithms are countable...
You do not need a different algorithm for each real.
Just take the algorithm that proves the statement for rational p. It proves the statement for all reals bigger than p. (hence having as many algorithms as there are rational (countably many) is enough)