# Is there anything in real world (nature) which is uncountable ( i. e. infinite but not countably infinite)? [duplicate]

In set theory I read that the sets are either finite or infinite. If they are infinite then there are also two categories countably infinite or uncountable. Natural numbers $\Bbb{N}$, integers $\Bbb{Z}$, rational numbers $\Bbb{Q}$ etc. are examples of countably infinite sets , whereas real numbers $\Bbb{R}$, irrational numbers are very well known examples of uncountable sets.

Today I was thinking about counting objects in our day to day life. That time I realize that we can count each and every object.

For example :

1) Suppose I decided to count number of sand particles on a beach, even though the number is huge but one can count them one by one. ( I also want to know that are they infinite or just finite ( a big natural number will be representing their quantity )).

2) Same thing when I think about number of leaves on big tree, they are definitely finite.

3) Stars in the sky ( I read on internet that there are approx $10^{24}$ stars in universe). etc.

Similarly many objects seems to be finite ( or countably infinite* ( * please correct me if I'm wrong)) .

So my question is do we have any object in real world which is uncountable.

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• As your examples show, it is not obvious to give an example of any physical collection which is even countably infinite as opposed to being enormously, but finitely, large. – Tom Collinge Jul 5 '17 at 10:32
• @TomCollinge true . +1 for this. – Math_Explorer Jul 5 '17 at 10:34
• The structure of space in the real world is not clear to science yet: it may ultimately be discrete or continuous, and bounded or unbounded. These questions matter to the cardinality of the set of points in space. – Ian Jul 5 '17 at 10:39
• @Ian Thanks for this info :) – Math_Explorer Jul 5 '17 at 10:43