Recently, my son pointed me to a link to a very charming video that gave a very elementary demonstration of the fact that the set of real numbers is uncountable. It got me thinking: How would I somehow ignore the video’s approach and my hyper-specialist inclinations (I am a retired mathematician with research in several areas) and prove that fact in a really elementary fashion. So I thought about it a bit and the pdf below summarizes my exploration. I think it’s really elementary with an absolute minimum of mathematical notation. It starts with an explanation of what the title even means. Read it here or download the file and see for yourself!