Tonight at supper, Youngest Daughter (age 5 1/2) asked me, "What is the name of the biggest number?"
With some excitement, I told her, "There isn't one! If you name any number, there is always a bigger one." After talking about this for a while, and using the word "infinity" a few times, I asked her, "Do you understand?"
"No," she said, fairly cheerfully. End of subject for the time.
After supper, she got out a pencil and paper. "I'm writing the numbers up to infinity," she told me.
"But you can't!" I said. "It's not possible."
"Yes, I can," she insisted. "I have a paper and pencil, and I'm going to write them." A little later, she added, "I'm going to write the numbers up to 500."
"That's not infinity," I said. "Do you know what 'infinity' means?"
"If a thing goes on forever, that means it goes on to infinity. Numbers go on to infinity, and that means they never end."
A little later, she told me that she was trying to write, "The fact is that things go on forever. They never end." But, she added, she couldn't remember how to spell "things." I suggested that "numbers" is easier to spell than "things." We talked for a bit about how to spell "numbers."
Then I said, "Besides, it depends on what things you're talking about. Some things do come to an end, but others don't."
"Cups come to an end!" she said.
"That's right. Cups come to an end. But numbers don't."
Next stop: Actual and potential infinities.