Comments on: A Quirky Introduction To Number Systems

By: Imran

Imran — Sun, 09 Feb 2020 16:48:48 +0000

Follow numbers in base 3 system. May be this will help: http://www.gwydir.demon.co....

By: Tianchi Liu

Tianchi Liu — Fri, 10 May 2019 17:17:16 +0000

Very Very interesting. Another analogy is, we want to read 1/3 from a 10 mark (unit length) ruler. We have to approximate this value by reading between two marks. However, it is trivial to read 1/3 from a 3 mark ruler. The read will be in align with the marker. I think the problem now becomes, is it even possible to create such a ruler with perfect marks.

By: UnderstandingMath

UnderstandingMath — Thu, 20 Sep 2018 10:46:11 +0000

I didn't understand the base 3 thing. Can anyone explain?

By: kalid

kalid — Fri, 18 Jul 2014 21:31:31 +0000

In reply to Smo.

Thanks Smo. I agree that we do have a well-defined definition of .999..., but most people are only accidentally using that definition. That is, kids who wonder what .999... means aren't thinking "Gee, can someone compute the limit of the following sequence: ..." but instead something like "What is the closest number I can get to 1 without (apparently) touching it?"

Intuitively, if you accept the idea of infinitesimals, you can say "There's a possibility of getting infinitely close without touching. Standing on the line doesn't mean you're playing in the field." and if you don't, you'd say "There's no way to represent an infinitely small gap, so you are either touching 1.0 or not, and .999... counts as touching. On the line is in the field.".