it will be fully available in a few days - 14

**A short discussion on the concepts**
**of discrete and continuum in mathematics,**
**and Zeno's paradoxes**

I decided to publish this short discussion (a synopsis of the two long
papers published in *Episteme* N. 8, http://www.dipmat.unipg.it/~bartocci/ep8/ep8.htm)
after discovering - I must add: with surprise! - that this kind of comments
were not easily available neither in my Geometry, Algebra and Analysis
text books, nor in Internet. Thus I hope that my effort will be useful
to other people looking for the same kind of information.

* * * * *

When looking for the meaning of the two __attributes__ of **discrete**
and **continuous** in mathematics, when applied to some specific "structure"
to be individuated (we do not mean, for instance, the concept of "continuous
function" in topology), one usually finds, in actual mathematical text
books:

1 - In __set theory__, one usually means that a *discrete* set
is either a *finite* set, or an *enumerable* one. Moreover, one
calls the *power of the continuum* the cardinality of the set of real
numbers *R*.

2 - In __topology__, *discrete* is used in order to indicate
a topological space in which each subset is open. A topological space is
said to be a *continuum*, if it is a *compact* (implying Hausdorff
separated) and *connected* (sometimes one adds: *metrizable*).

See for instance:

http://www.virtualology.com/virtualpubliclibrary/hallofeducation/Mathematics/pointsettopology.com/

3 - In the __theory of ordered fields__, one calls *continuum*
the unique, up to isomorphisms, *ordered complete archimedean field*
of real numbers *R*.

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