Re: Extending the reals

cbrown@xxxxxxxxxxxxxxxxx wrote:

For the third time in this thread, "dense", "connected", and
"continuous" have different meanings. And "gapless" has no particular
meaning to me at all; unless it is supposed to mean "dense".


So is it a complete ordered field?

Otherwise there's not the arithmetic on it, defying its stated
properties.

Sets are defined by their elements and N in the generic extension
bijects to R. Transfinite cardinals is finitism.

The real numbers are _definitely_ useful, and _widely_ used. They're
just not standard yet.

Ross

.

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