Question #3136f

1 Answer
Jun 21, 2016

Answer:

No - no number, except #0# itself.

Explanation:

If I understand your question properly, you're asking if you can divide a number by #2# until you get to #0#. That is impossible for real numbers, with the exception of #0# (because #0# divided by anything is #0#).

The reason for this, intuitively, is that you can't generate nothing from something. If you were able to change a number like #20# to #0# by dividing it by #2# over and over, imagine what that would mean in real life. You would be able to take, say, #20# pencils and divide them into groups until you either had #0# groups or #0# pencils in each group, neither of which is possible, because that would mean you have #0# 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 #1#, by dividing powers of #2# (#2#, #4#, #8#, #16#, etc) by #2# until you hit #1#. For example
#64/2=32#
#32/2=16#
#16/2=8#
#8/2=4#
#4/2=2#
#2/2=1#

If you were to keep going, you would get #0.5#, then #0.25#, then #0.125# - closer and closer to #0# - but you would never actually hit #0#.

Technically, you could get infinitely close to #0# by dividing by #2# infinitely many times. But you can't actually get to #0# 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 #0#. 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.