product of the probabilities of all the symbols that we that we encode it and so if we so this is some natural number and if we code the natural number the number of bits needed is about the log of the number that's the log base 2 of the number that's how many bits we need to code it so we see that this is this is the code length it's the sum over T of log 1 over P for all the symbols and so so if we take this and we divide by the number of symbols so if we take this divided by the number of symbols you see that this goes to the entropy of this of