Question #3136f

1 Answer
Jun 21, 2016

No - no number, except 00 itself.

Explanation:

If I understand your question properly, you're asking if you can divide a number by 22 until you get to 00. That is impossible for real numbers, with the exception of 00 (because 00 divided by anything is 00).

The reason for this, intuitively, is that you can't generate nothing from something. If you were able to change a number like 2020 to 00 by dividing it by 22 over and over, imagine what that would mean in real life. You would be able to take, say, 2020 pencils and divide them into groups until you either had 00 groups or 00 pencils in each group, neither of which is possible, because that would mean you have 00 pencils. In order for a group to exist, you need to have something in that group. I know I might be flirting with empty-set theory and high-level stuff here, but the basic idea is you can't divide something until there's nothing left.

The lowest number whole number you can get to is 11, by dividing powers of 22 (22, 44, 88, 1616, etc) by 22 until you hit 11. For example
64/2=32642=32
32/2=16322=16
16/2=8162=8
8/2=482=4
4/2=242=2
2/2=122=1

If you were to keep going, you would get 0.50.5, then 0.250.25, then 0.1250.125 - closer and closer to 00 - but you would never actually hit 00.

Technically, you could get infinitely close to 00 by dividing by 22 infinitely many times. But you can't actually get to 00 because, as I said before, you can't get nothing from something.

The paradox of Zeno of Elea, regarding the flight of an arrow, was essentially based on the fallacy that you could divide something up infinitely many times and eventually end up with 00. If you know calculus, or will in the future, you'll know/learn that even infinitely many segments can be added up and come out to a number.