Oct
14 |
comment |
Existence of a non-null-homotopic simple closed curve
Cont. (finish): The z=0 level curve cannot be contracted because an infinite sequence of the level z=0 points would have to reach the top level z=1 at about the same time during the homotopy. This reaching z=1 would be forced by elementary considerations or by a simple homological argument. |
Oct
14 |
comment |
Existence of a non-null-homotopic simple closed curve
Every simple curve is contained in one of the cones. (The example is fine and elegant, of course). |
Oct
9 |
comment |
Has philosophy ever clarified mathematics?
The link to the above: en.wikiquote.org/wiki/Carl_Friedrich_Gauss |
Oct
9 |
comment |
Has philosophy ever clarified mathematics?
@GerryMyerson, a more solid quote: I am almost amazed that you consider a professional philosopher capable of no confusion in concepts and definitions. ... even in Kant it is often not much better; in my opinion his distinction between analytic and synthetic theorems is such a one that either peters out in a triviality or is false. ####### As quoted in Carl Friedrich Gauss: Titan of Science (1955) by Guy Waldo Dunnington. p. 362 |
Oct
9 |
comment |
Has philosophy ever clarified mathematics?
Links to the above (possible interdependent) are: ** www-groups.dcs.st-and.ac.uk/history/Quotations/Gauss.html ** brainyquote.com/quotes/authors/c/carl_friedrich_gauss.html ** brainyquote.com/quotes/quotes/c/carlfriedr319904.html ***** I'll provide a different one, which goes kinto more details. |
Oct
9 |
comment |
Has philosophy ever clarified mathematics?
@GerryMyerson, several links give the following: When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false. I'll provide a more detailed quote too. |
Sep
27 |
revised |
Is there an algebraic approach to metric spaces?
added 160 characters in body |
Sep
27 |
comment |
Is there an algebraic approach to metric spaces?
In Kaplansky's paper, given two elements $f\ g$ of a Kaplansky's lattice, distance $\ d := d(f\ g)\ $ is a non-negative real number such that $\ g-c\subseteq f\subseteq g+c\ $ for $\ c=d\ $ but not for any non-negative real number $\ c < d.\ $ In the general case of d-lattices the value $\ d\ $ may be infinite. |
Sep
22 |
comment |
Proof for new deterministic primality test
@JeppeStigNielsen -- thank you. *** (Not all my q's are hard :-) ). |
Sep
14 |
accepted | Can an acyclic continuum be metrically homogenous? (I'd say: no way! :-) |
Sep
14 |
revised |
Can an acyclic continuum be metrically homogenous? (I'd say: no way! :-)
trivial assumption |
Sep
12 |
comment |
Proof for new deterministic primality test
Is one of the implications true? |
Sep
8 |
comment |
An infinite set in a compact space
$X = \{0\}$ -- isn't this true? |
Aug
24 |
comment |
Countable path-connected Hausdorff space
Right, Joel - Urysohn's function. Thank you Todd for pointing me to Joel's answer. (Frankly, the q. posed above should never be considered "research"). |
Aug
12 |
awarded | Nice Answer |
Aug
11 |
awarded | Yearling |
Aug
11 |
comment |
Mathematical software wish list
When you enter url like abc.HTML in an browser then you see the html-formatted text. *** When you enter url like abc.tex in a latex browser than you see the latex-formatted file. |
Aug
10 |
comment |
Mathematical software wish list
What is an HTML browser? |
Aug
8 |
answered | Mathematical software wish list |
Aug
8 |
answered | Mathematical software wish list |