Resources for Learning Hyperreal Numbers












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I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.



What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.



Thanks.






nonstandard-analysis







share|cite|improve this question









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  • $begingroup$
    The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
    $endgroup$
    – InequalitiesEverywhere
    Jan 1 at 12:20






  • 3




    $begingroup$
    also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
    $endgroup$
    – Masacroso
    Jan 1 at 12:22










  • $begingroup$
    Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
    $endgroup$
    – Mark S.
    Jan 1 at 14:03
















3












$begingroup$


I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.



What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.



Thanks.






nonstandard-analysis







share|cite|improve this question









$endgroup$












  • $begingroup$
    The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
    $endgroup$
    – InequalitiesEverywhere
    Jan 1 at 12:20






  • 3




    $begingroup$
    also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
    $endgroup$
    – Masacroso
    Jan 1 at 12:22










  • $begingroup$
    Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
    $endgroup$
    – Mark S.
    Jan 1 at 14:03














3












3








3


1



$begingroup$


I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.



What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.



Thanks.






nonstandard-analysis







share|cite|improve this question









$endgroup$




I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.



What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.



Thanks.






nonstandard-analysis




nonstandard-analysis






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 1 at 12:03









HarrisonOHarrisonO

414




414












  • $begingroup$
    The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
    $endgroup$
    – InequalitiesEverywhere
    Jan 1 at 12:20






  • 3




    $begingroup$
    also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
    $endgroup$
    – Masacroso
    Jan 1 at 12:22










  • $begingroup$
    Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
    $endgroup$
    – Mark S.
    Jan 1 at 14:03


















  • $begingroup$
    The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
    $endgroup$
    – InequalitiesEverywhere
    Jan 1 at 12:20






  • 3




    $begingroup$
    also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
    $endgroup$
    – Masacroso
    Jan 1 at 12:22










  • $begingroup$
    Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
    $endgroup$
    – Mark S.
    Jan 1 at 14:03
















$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20




$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20




3




3




$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22




$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22












$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03




$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03










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