[sykh]

Let S be an encoding of the works of Shakespeare in binary. A normal number contains S in its binary expansion. We can do this for all information. In this sense is it correct to say that a normal number contains infinite information in it?

[chriswarbo]

Again, depends on your definition of information. For shannon information, you would need to define a protocol. If the protocol is "I will send you the entire works of Shakespeare" then I would be sending you no information. Likewise, if the protocol is to send you S, then S contains no information.