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Topic: Foundations of real numbers
Replies: 26   Last Post: Oct 14, 2012 7:35 PM

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G. A. Edgar

Posts: 2,494
Registered: 12/8/04
Re: Foundations of real numbers
Posted: Oct 12, 2012 9:40 AM
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For the beginning of a subject, sometimes the choices made are limited.

For example: I can imagine* a textbook that begins by postulating a
complete ordered field R. (Complete in the order sense.) Then
constructing, within R, the set N or natural numbers. Sometime later
defining "sequence" as a function with domain N. And only still later
defining "Cauchy" sequence. So, for this arrangement the least upper
bound axiom makes perfect sense.

* Perhaps called CALCULUS, written by M. Spivak ...

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/


Date Subject Author
10/10/12
Read Foundations of real numbers
Paul
10/10/12
Read Re: Foundations of real numbers
Ken.Pledger@vuw.ac.nz
10/13/12
Read Re: Foundations of real numbers
Graham Cooper
10/13/12
Read Re: Foundations of real numbers
Frederick Williams
10/13/12
Read Re: Foundations of real numbers
Graham Cooper
10/11/12
Read Re: Foundations of real numbers
Peter Webb
10/11/12
Read Re: Foundations of real numbers
Shmuel (Seymour J.) Metz
10/11/12
Read Re: Foundations of real numbers
Michael Stemper
10/12/12
Read Re: Foundations of real numbers
Peter Webb
10/12/12
Read Re: Foundations of real numbers
Virgil
10/12/12
Read Re: Foundations of real numbers
LudovicoVan
10/12/12
Read Re: Foundations of real numbers
Michael Stemper
10/12/12
Read Re: Foundations of real numbers
Peter Webb
10/13/12
Read Re: Foundations of real numbers
Shmuel (Seymour J.) Metz
10/12/12
Read Re: Foundations of real numbers
Shmuel (Seymour J.) Metz
10/12/12
Read Re: Foundations of real numbers
Peter Webb
10/13/12
Read Re: Foundations of real numbers
Peter Webb
10/13/12
Read Re: Foundations of real numbers
Frederick Williams
10/11/12
Read Re: Foundations of real numbers
Robin Chapman
10/11/12
Read Re: Foundations of real numbers
Frederick Williams
10/11/12
Read Re: Foundations of real numbers
Frederick Williams
10/11/12
Read Re: Foundations of real numbers
Herman Rubin
10/11/12
Read Re: Foundations of real numbers
Michael Stemper
10/11/12
Read Re: Foundations of real numbers
Brian Q. Hutchings
10/12/12
Read Re: Foundations of real numbers
G. A. Edgar
10/14/12
Read Re: Foundations of real numbers
gnasher729
10/14/12
Read Re: Foundations of real numbers
Graham Cooper

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