39 ms·
Hrm, I can't tell if you're joking, but the existence (or non-existence) of infinitesimals is an axiom: http://en.wikipedia.org/wiki/Archimedean_property http:
by kalid 15y ago
Hrm, I can't tell if you're joking, but the existence (or non-existence) of infinitesimals is an axiom:
http://en.wikipedia.org/wiki/Archimedean_property http://en.wikipedia.org/wiki/Archimedean_property
It took thousands of years to accept that the parallel postulate might not be required, and lots of neat geometry emerged. Why not have number systems where infinitesimals are allowed?
- bostonpete 15y agoActually, if you look at the original version of that page (http://en.wikipedia.org/w/index.php?title=Archimedean_property&oldid=1130647 http://en.wikipedia.org/w/index.php?title=Archimedean_proper...), it doesn't mention the word "axiom" at all. Someone edited the page at some point to introduce this concept! It seems to have been done in a somewhat anonymous fashion, lending credence to Natsu's theory that there's a conspiracy involved here.
- derleth 15y ago> Why not have number systems where infinitesimals are allowed? There are. A few of them, in fact. Look up the hyperreals.
- kalid 15y agoYep, exactly :). (Should have made it more clear that I was referring to other systems like surreals and hyperreals, but wasn't clear whether the parent was joking or not).
- Natsu 15y agoI think you might like this: http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml
- kalid 15y agoThanks for the pointer! I enjoy discussions about .999... because it really makes us question what we mean about infinity (and assumptions about the reals).