No Smallest Positive Real

I asked "Is there a smallest positive real number. Why or why not?"

A student wrote: "There is no smallest positive real number, because if you thought you had found the smallest positive real number, you could divide it in half a get a smaller one."

Full credit.

But he went on: "Then you can take the result of that calculation, divide it in half and get still a smaller one. Then you can divide in half again to get something still smaller. Then you can do it again. This process generates a sequence that goes on forever. It is infantile."