It's simple for you mathematicians, but I'm a physician, I don't know much about set theory or logic and such, so it's difficult for me. Let M be the set of all integers that can be described in English in, say, ten lines of text. For example, "fourteen" or "seventy minus eight" or "832832541872 to the power of 784315" are all numbers belonging to M. Let k be the largest number in this set. Since in ten lines of text you have a large, but finite, combination of characters, and since not all combinations are meaningful in English, and certainly not all combinations describe a number, then k exists and it's finite. Let m be k plus one. I have described, in less than ten lines of text, a number that it's larger than the largest number that can be described in ten lines of (bad, I'm sorry) English text. Explanations?