Re: teminology

On 13-04-2007 10:06, gius wrote:

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 ?

There is no precise definition of that. If, for instance, you define
f:N ---> R by f(n) = n, then a natural way of extending _f_ into
a function from R into R is by defining f(x) = x for all _x_. An
artificial way of doing the same thing is, for instance, by defining
f(x) = x is _x_ us natural and f(x) = 1 otherwise.

If you want mare precise information, then you should provide the
context that you are working in.

Best regards,

Jose Carlos Santos
.

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