Re: teminology

In article <1176455217.528539.209410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"gius" <giu.giorgi@xxxxxxxxx> wrote:

Hi, everyone,

In mathematics,
what does it mean for a map defined in a certain set,
say A,
to extend "naturally" to a set B which contains as a proper subset
the set A ?


It means the "obvious" extension. It's the extension 10 out of 10
mathematicians would pick if you asked them. In other words there's not
always a precise definition, but it's obvious.

Example: f:N->N given by f(n) = n, where N is the naturals. How would
you extend that "naturally" to the reals? Obviously you'd pick the
identity function on the reals; even though there are uncountably many
other extensions that take the same values on N.

Does that help?
.

Relevant Pages

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  • Re: teminology
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